Thursdays at 3.30 p.m. in the

Lecture room on the 1st floor of the DIAS building at

10 Burlington Road

Please visit also the STP event webpage for information about further seminars in conferences and meetings.

The Maths Department at Trinity College Dublin also has a list of forthcoming seminars here.

The Computational Applied Mathematics Seminars in TCD has its list of forthcoming seminars here.

Seminars during the last years: 2006.

Tuesday Dec 01, at 3.30 p.m.

Prof. Kumar Gupta, Saha Institute, Kolkota

Wednesday Dec 02, at 4:30 p.m.

Dr. Jonathan Shock, Santiago

Abstract:

We study the holographic D3/D7 setup dual to N=4 supersymmetric Yang-Mills with quenched fundamental matter. We extend the previous analyses of conductivity and photoproduction to the case where there is a finite electric field. Due to the electric field a special region in the D7-brane geometry, labelled the singular shell, appears generically, and the computation of correlators involves a careful study of the indicial exponents both at this singular region and at the horizon. We show that there is a unique choice consistent with the known expression for the electrical conductivity found by Karch and O'Bannon. We explore the parameter space spanned by the quark mass, the baryon density and the electric field. We find a region where the conductivity and photoproduction change rapidly and trace this behavior to competing effects which manifest themselves as a crossover behavior in the probe brane embeddings.

Abstract:

We study the holographic D3/D7 setup dual to N=4 supersymmetric Yang-Mills with quenched fundamental matter. We extend the previous analyses of conductivity and photoproduction to the case where there is a finite electric field. Due to the electric field a special region in the D7-brane geometry, labelled the singular shell, appears generically, and the computation of correlators involves a careful study of the indicial exponents both at this singular region and at the horizon. We show that there is a unique choice consistent with the known expression for the electrical conductivity found by Karch and O'Bannon. We explore the parameter space spanned by the quark mass, the baryon density and the electric field. We find a region where the conductivity and photoproduction change rapidly and trace this behavior to competing effects which manifest themselves as a crossover behavior in the probe brane embeddings.

Friday Dec 04, at 3.30 p.m.

Dr. Anton Khoroshkin, ETH Zurich, Dept. of Mathematics

Abstract:

I will discuss some results on the cohomology of the Lie algebra of formal vector fields on the plane and some related Lie algebras, and applications of these results to formal differential geometry. If time allows, I will also explain how to use these results to construct central extensions of a 2-dimensional generalization of the Witt algebra.

Abstract:

I will discuss some results on the cohomology of the Lie algebra of formal vector fields on the plane and some related Lie algebras, and applications of these results to formal differential geometry. If time allows, I will also explain how to use these results to construct central extensions of a 2-dimensional generalization of the Witt algebra.

Tuesday Dec 10, at 3.30 p.m.

Dr. Marco Panero, ETH Zurich, Switzerland

Abstract:

The experimental evidence gathered in high-energy collisions of heavy ions at SPS and RHIC has revealed that, at high temperature, hadronic matter undergoes a qualitative change to a new state, characterized by surprising features making it a nearly ideal fluid. Some properties of this `strongly interacting quark-gluon plasma' can be predicted numerically by computer simulations of lattice QCD, but a full analytical description based on the first principles of QCD has proven elusive. In recent years, however, new analytical insights into the dynamics of strongly interacting systems came from String Theory, with gauge/gravity techniques based on the AdS/CFT correspondence conjectured by Maldacena, and involving the mathematical simplifications that occur when the rank of the gauge group is taken to infinity. In this talk, after introducing the physical problem of the QCD plasma and briefly discussing the lattice formulation for finite-temperature QCD studies, I shall present the results of my recent simulations of the equation of state in SU(N) gauge theories with N = 3, 4, 5, 6 and 8 colors, and their extrapolation to the limit for N going to infinity. The results for the different gauge groups reveal that the equilibrium thermodynamic observables, normalized according to the number of gluons, are weakly dependent on N (the `physical case' N = 3 being already very close to the large-N limit), and can be successfully described by holographic gauge/gravity models. The implications of these findings for a potentially realistic stringy description of the QCD plasma, as well as some open problems for future research, will be pointed out. This talk is based on arXiv:0907.3719 [hep-lat].

Abstract:

The experimental evidence gathered in high-energy collisions of heavy ions at SPS and RHIC has revealed that, at high temperature, hadronic matter undergoes a qualitative change to a new state, characterized by surprising features making it a nearly ideal fluid. Some properties of this `strongly interacting quark-gluon plasma' can be predicted numerically by computer simulations of lattice QCD, but a full analytical description based on the first principles of QCD has proven elusive. In recent years, however, new analytical insights into the dynamics of strongly interacting systems came from String Theory, with gauge/gravity techniques based on the AdS/CFT correspondence conjectured by Maldacena, and involving the mathematical simplifications that occur when the rank of the gauge group is taken to infinity. In this talk, after introducing the physical problem of the QCD plasma and briefly discussing the lattice formulation for finite-temperature QCD studies, I shall present the results of my recent simulations of the equation of state in SU(N) gauge theories with N = 3, 4, 5, 6 and 8 colors, and their extrapolation to the limit for N going to infinity. The results for the different gauge groups reveal that the equilibrium thermodynamic observables, normalized according to the number of gluons, are weakly dependent on N (the `physical case' N = 3 being already very close to the large-N limit), and can be successfully described by holographic gauge/gravity models. The implications of these findings for a potentially realistic stringy description of the QCD plasma, as well as some open problems for future research, will be pointed out. This talk is based on arXiv:0907.3719 [hep-lat].

Thursday Oct 29, at 3.30 p.m.

Matthew Headrick, Brandeis

Wednesday Oct 28, at 3.30 p.m.

Prof. Nick Evans,

School of Physics & Astronomy University of Southampton

School of Physics & Astronomy University of Southampton

Tuesday Oct 06, at 3.30 p.m.

Dr. Andrew O'Bannon, Max Planck Institute Fur Physics, Munich

Abstract:

Gauge-gravity duality is an extremely useful tool for studying strongly-coupled gauge theories, and has many applications to real-world systems, such as the quark-gluon plasma and quantum critical points. Most gauge-gravity dualities involve a gauge theory with fields only in the adjoint representation of the gauge group. In many strongly-coupled systems, however, such as the quark-gluon plamsa, fields in the fundamental representation of the gauge group, "flavor fields," are crucially important. For (3+1)-dimensional gauge theories with gravity duals (AdS5/CFT4), the supergravity description of flavor fields is well-understood: flavor fields appear in supergravity as probe D-branes in AdS5. The story for (2+1)-dimensional gauge theories (AdS4/CFT3) is much less developed. Indeed, for supergravity on AdS4 x S7, the dual (2+1)-dimensional field theory (without flavor) was only recently discovered. In this talk I will describe how to add flavor to this theory. In particular, I will present a general recipe to determine the field theory, and in particular the couplings of the flavor fields, given a probe D-brane in AdS4.

Abstract:

Gauge-gravity duality is an extremely useful tool for studying strongly-coupled gauge theories, and has many applications to real-world systems, such as the quark-gluon plasma and quantum critical points. Most gauge-gravity dualities involve a gauge theory with fields only in the adjoint representation of the gauge group. In many strongly-coupled systems, however, such as the quark-gluon plamsa, fields in the fundamental representation of the gauge group, "flavor fields," are crucially important. For (3+1)-dimensional gauge theories with gravity duals (AdS5/CFT4), the supergravity description of flavor fields is well-understood: flavor fields appear in supergravity as probe D-branes in AdS5. The story for (2+1)-dimensional gauge theories (AdS4/CFT3) is much less developed. Indeed, for supergravity on AdS4 x S7, the dual (2+1)-dimensional field theory (without flavor) was only recently discovered. In this talk I will describe how to add flavor to this theory. In particular, I will present a general recipe to determine the field theory, and in particular the couplings of the flavor fields, given a probe D-brane in AdS4.

Thursday Sep 24, at 3.30 p.m.

Steven H. Simon, Oxford

Friday Aug 07, at 3.30 p.m.

Dr. Rene Meyer , Max Planck Institute Fur Physics, Munich

Abstract:

I will outline the derivation of a bosonic matrix model valid in the Friedmann-Robertson-Walker universe, based on several phenomenological assumptions. I will give a semiclassical argument for the emergence of space-time during the expansion of the universe, starting from the big bang singularity. This talk is based on the paper hep-th/0705.1586.

Abstract:

I will outline the derivation of a bosonic matrix model valid in the Friedmann-Robertson-Walker universe, based on several phenomenological assumptions. I will give a semiclassical argument for the emergence of space-time during the expansion of the universe, starting from the big bang singularity. This talk is based on the paper hep-th/0705.1586.

Thursday May 28, at 3.30 p.m.

Dr. Alexander Alexandrov, IHES, Bures-sur-Yvette, France

Abstract:

This is a brief review of recent progress in constructing solutions to the matrix model Virasoro equations. Various branches of matrix model partition function can be represented as intertwined products of universal elementary constituents: Gaussian partition functions Z_G and Kontsevich tau-functions Z_K. Technically, decomposition formulas are related to representation theory of algebras of Krichever-Novikov type on families of spectral curves with additional Seiberg-Witten structure. Representations of these algebras are encoded in terms of "the global partition functions". They interpolate between Z_G and Z_K associated with different singularities on spectral Riemann surfaces.

Abstract:

This is a brief review of recent progress in constructing solutions to the matrix model Virasoro equations. Various branches of matrix model partition function can be represented as intertwined products of universal elementary constituents: Gaussian partition functions Z_G and Kontsevich tau-functions Z_K. Technically, decomposition formulas are related to representation theory of algebras of Krichever-Novikov type on families of spectral curves with additional Seiberg-Witten structure. Representations of these algebras are encoded in terms of "the global partition functions". They interpolate between Z_G and Z_K associated with different singularities on spectral Riemann surfaces.

Thursday May 21, at 3.30 p.m.

Dr. Govind Krishnaswami,

Durham

Abstract:

We try to use scale-invariance and the large-N limit to find a non-trivial 4d O(N) scalar field model with controlled UV behavior and naturally light scalar excitations. The principle is to fix interactions by requiring the effective action for space-time dependent background fields to be finite and scale-invariant when regulators are removed. We find a line of non-trivial UV fixed-points in the large-N limit, parameterized by a dimensionless coupling. They reduce to classical lambda phi^4 theory when hbar vanishes. For hbar >0, neither action nor measure is scale invariant, but the effective action is. Scale invariance makes it natural to set a mass deformation to zero. The model has phases where O(N) invariance is unbroken or spontaneously broken. Masses of the lightest excitations above the unbroken vacuum are found. We derive a non-linear equation for oscillations about the broken vacuum. The interaction potential is shown to have a locality property at large-N. In 3d, our construction reduces to the line of large-N fixed points in |phi|^6 theory.

Durham

Abstract:

We try to use scale-invariance and the large-N limit to find a non-trivial 4d O(N) scalar field model with controlled UV behavior and naturally light scalar excitations. The principle is to fix interactions by requiring the effective action for space-time dependent background fields to be finite and scale-invariant when regulators are removed. We find a line of non-trivial UV fixed-points in the large-N limit, parameterized by a dimensionless coupling. They reduce to classical lambda phi^4 theory when hbar vanishes. For hbar >0, neither action nor measure is scale invariant, but the effective action is. Scale invariance makes it natural to set a mass deformation to zero. The model has phases where O(N) invariance is unbroken or spontaneously broken. Masses of the lightest excitations above the unbroken vacuum are found. We derive a non-linear equation for oscillations about the broken vacuum. The interaction potential is shown to have a locality property at large-N. In 3d, our construction reduces to the line of large-N fixed points in |phi|^6 theory.

Wednesday May 20, at 3.30 p.m.

Dr. Mathias Kaminski,

Universidad Autonoma de Madrid, Madrid, Spain

Abstract:

Recently the gauge/gravity duality has been successfully used in bottom-up approaches in order to model effects known from strongly correlated electron systems, such as the (quantum) Hall effect and superconductivity/superfluidity. In this talk I will present one of these bottom-up approaches with a condensing scalar and comment on its hydrodynamic modes. Nevertheless, my main focus will be on a top- down approach showing that in a strongly-coupled thermal field theory with flavor at high isospin density a new phase emerges. This new phase displays signatures of superconductivity such as an infinite dc conductivity and an energy gap. The advantage of the top- down approach is that it allows to give a direct identification of, and a gravity explanation for the behavior of the fundamental degrees of freedom in the field theory at strong coupling. In particular we identify the Cooper pairs and the pairing mechanism. We will review these recent predictions and the basic concepts needed to derive them.

Universidad Autonoma de Madrid, Madrid, Spain

Abstract:

Recently the gauge/gravity duality has been successfully used in bottom-up approaches in order to model effects known from strongly correlated electron systems, such as the (quantum) Hall effect and superconductivity/superfluidity. In this talk I will present one of these bottom-up approaches with a condensing scalar and comment on its hydrodynamic modes. Nevertheless, my main focus will be on a top- down approach showing that in a strongly-coupled thermal field theory with flavor at high isospin density a new phase emerges. This new phase displays signatures of superconductivity such as an infinite dc conductivity and an energy gap. The advantage of the top- down approach is that it allows to give a direct identification of, and a gravity explanation for the behavior of the fundamental degrees of freedom in the field theory at strong coupling. In particular we identify the Cooper pairs and the pairing mechanism. We will review these recent predictions and the basic concepts needed to derive them.

Thursday April 30, at 3.30 p.m.

Dr. Roberto Auzzi,

Swansea

Abstract:

We study magnetic flux tubes in the Higgs vacuum of the N=1^* mass deformation of SU(N_c), N=4 SYM and its large N_c string dual, the Polchinski-Strassler geometry. Choosing equal masses for the three adjoint chiral multiplets, for all N_c we identify a "colour-flavour locked" symmetry, SO(3)_{C+F} which leaves the Higgs vacuum invariant. At weak coupling, we find explicit non-Abelian k-vortex solutions carrying a Z_{N_c}-valued magnetic flux, with winding, 0 < k < N_c. These k-strings spontaneously break SO(3)_{C+F} to U(1)_{C+F} resulting in an S^2 moduli space of solutions. The world-sheet sigma model is a nonsupersymmetric CP^1 model with a theta angle \theta_{1+1} = k(N_c-k)\theta_{3+1} where \theta_{3+1} is the Yang-Mills vacuum angle. We find numerically that k-vortex tensions follow the Casimir scaling law T_k \propto k (N_c-k) for large N_c. In the large N_c IIB string dual, the SO(3)_{C+F} symmetry is manifest in the geometry interpolating between AdS_5 x S^5 and the interior metric due to a single D5-brane carrying D3-brane charge. We identify candidate k-vortices as expanded probe D3-branes formed from a collection of k D-strings. The resulting k-vortex tension exhibits precise Casimir scaling, and the effective world-sheet theta angle matches the semiclassical result. S-duality maps the Higgs to the confining phase so that confining string tensions at strong 't Hooft coupling also exhibit Casimir scaling in N=1^* theory in the large N_c limit.

Swansea

Abstract:

We study magnetic flux tubes in the Higgs vacuum of the N=1^* mass deformation of SU(N_c), N=4 SYM and its large N_c string dual, the Polchinski-Strassler geometry. Choosing equal masses for the three adjoint chiral multiplets, for all N_c we identify a "colour-flavour locked" symmetry, SO(3)_{C+F} which leaves the Higgs vacuum invariant. At weak coupling, we find explicit non-Abelian k-vortex solutions carrying a Z_{N_c}-valued magnetic flux, with winding, 0 < k < N_c. These k-strings spontaneously break SO(3)_{C+F} to U(1)_{C+F} resulting in an S^2 moduli space of solutions. The world-sheet sigma model is a nonsupersymmetric CP^1 model with a theta angle \theta_{1+1} = k(N_c-k)\theta_{3+1} where \theta_{3+1} is the Yang-Mills vacuum angle. We find numerically that k-vortex tensions follow the Casimir scaling law T_k \propto k (N_c-k) for large N_c. In the large N_c IIB string dual, the SO(3)_{C+F} symmetry is manifest in the geometry interpolating between AdS_5 x S^5 and the interior metric due to a single D5-brane carrying D3-brane charge. We identify candidate k-vortices as expanded probe D3-branes formed from a collection of k D-strings. The resulting k-vortex tension exhibits precise Casimir scaling, and the effective world-sheet theta angle matches the semiclassical result. S-duality maps the Higgs to the confining phase so that confining string tensions at strong 't Hooft coupling also exhibit Casimir scaling in N=1^* theory in the large N_c limit.

Thursday April 23, at 3.30 p.m.

Dr. Oliver J. Rosten,

Sussex University

Abstract:

Drawing on analogies with the commutative case, the Wilsonian picture of renormalization is developed for noncommutative scalar field theory. The dimensionful noncommutativity parameter, theta, induces several new features. Fixed-points are replaced by `floating-points' (actions which are scale independent only up to appearances of theta written in cutoff units). Furthermore, it is found that one must use correctly normalized operators, with respect to a new scalar product, to define the right notion of relevance and irrelevance.

Sussex University

Abstract:

Drawing on analogies with the commutative case, the Wilsonian picture of renormalization is developed for noncommutative scalar field theory. The dimensionful noncommutativity parameter, theta, induces several new features. Fixed-points are replaced by `floating-points' (actions which are scale independent only up to appearances of theta written in cutoff units). Furthermore, it is found that one must use correctly normalized operators, with respect to a new scalar product, to define the right notion of relevance and irrelevance.

Thursday March 19, at 3.30 p.m.

Dr. Veselin Filev,

DIAS

Abstract:

I focus on the effective action of the pseudo-Goldstone modes for Dp/Dq systems in external magnetic field and study both numerically and analytically the corresponding dispersion relations. In the D3/D7 case one observes GMOR relation, while the D3/D5 system exhibits dispersion relation characteristic of magnon spin waves in ferromagnetic. I briefly discuss some universal properties of the spontaneous symmetry breaking mechanism in Dp/Dq systems.

DIAS

Abstract:

I focus on the effective action of the pseudo-Goldstone modes for Dp/Dq systems in external magnetic field and study both numerically and analytically the corresponding dispersion relations. In the D3/D7 case one observes GMOR relation, while the D3/D5 system exhibits dispersion relation characteristic of magnon spin waves in ferromagnetic. I briefly discuss some universal properties of the spontaneous symmetry breaking mechanism in Dp/Dq systems.

Monday March 2, at 12.00

Neil Lambert

Department of Mathematics, King's College London

Department of Mathematics, King's College London

Thursday January 29, at 3.30 p.m.

Prof. Carlos Nunez

Swansea University

Abstract:

I will discuss some recent advances on the duality between gauge field theories and strings.

Swansea University

Abstract:

I will discuss some recent advances on the duality between gauge field theories and strings.

Thursday November 20, at 3.30 p.m. at Third Floor Discussion Room- Note unusual room.

Dr. Jonathan Shock, IGFAE Spain

Abstract:

Using the AdS/CFT correspondence, we compute the spectral functions of thermal super Yang Mills at large N_c coupled to a small number of flavours of fundamental matter, in the presence of a nonzero baryon density. The holographic dual of such a theory involves the addition of probe D7-branes with a background worldvolume gauge field switched on, embedded in the geometry of a stack of black D3-branes. We perform the analysis in the vector and scalar channels which become coupled for nonzero values of the spatial momentum and baryon density. In addition, we obtain the effect of the presence of net baryon charge on the photon production. We also extract the conductivity and find perfect agreement with the results derived in a macroscopic setup.

Abstract:

Using the AdS/CFT correspondence, we compute the spectral functions of thermal super Yang Mills at large N_c coupled to a small number of flavours of fundamental matter, in the presence of a nonzero baryon density. The holographic dual of such a theory involves the addition of probe D7-branes with a background worldvolume gauge field switched on, embedded in the geometry of a stack of black D3-branes. We perform the analysis in the vector and scalar channels which become coupled for nonzero values of the spatial momentum and baryon density. In addition, we obtain the effect of the presence of net baryon charge on the photon production. We also extract the conductivity and find perfect agreement with the results derived in a macroscopic setup.

Tuesday November 4, at 4.30 p.m. - Note changed time.

Dr. Vladimir S.
Malinovsky,

MagiQ Technologies, Inc., New York

Abstract:

A new method of entangled states preparation of two-qubit systems is proposed. The method combines the techniques of coherent control by manipulation of the relative phase between pulses, and adiabatic control using time-delayed pulse sequences. In this work we exploit the sensitivity of population dynamics to the relative phase of the fields in order to control entanglement. The interplay between adiabatic partially time-delayed pulse sequences and phase control allow to prepare any type of entangled state in a simple and robust manner. We show that the population and entanglement exhibits collapses and full revivals when the initial distribution of phonons is a coherent state. A scheme to generate phase-controlled two-qubit gates based on the effect of full revivals is proposed.

MagiQ Technologies, Inc., New York

Abstract:

A new method of entangled states preparation of two-qubit systems is proposed. The method combines the techniques of coherent control by manipulation of the relative phase between pulses, and adiabatic control using time-delayed pulse sequences. In this work we exploit the sensitivity of population dynamics to the relative phase of the fields in order to control entanglement. The interplay between adiabatic partially time-delayed pulse sequences and phase control allow to prepare any type of entangled state in a simple and robust manner. We show that the population and entanglement exhibits collapses and full revivals when the initial distribution of phonons is a coherent state. A scheme to generate phase-controlled two-qubit gates based on the effect of full revivals is proposed.

Thursday, 18 September 2008, at 3.30 p.m.

Matthias Christandl,

Cambridge Center for Quantum Computation

Abstract:

We propose a general method for studying properties of quantum channels acting on an n-partite system, whose action is invariant under permutations of the subsystems. Our main result is that, in order to prove that a certain property holds for any arbitrary input, it is sufficient to consider the special case where the input is a particular de Finetti-type state, i.e., a state which consists of n identical and independent copies of an (unknown) state on a single subsystem. Our method can be applied to the analysis of information-theoretic problems. For example, in quantum cryptography, we get a simple proof for the fact that security of a discrete-variable quantum key distribution protocol against collective attacks implies security of the protocol against the most general attacks. The resulting security bounds are tighter than previously known bounds obtained by proofs relying on the exponential de Finetti theorem. We note that our results can be generalised to quantum channels that commute with the action of an arbitrary finite or compact group.

Cambridge Center for Quantum Computation

Abstract:

We propose a general method for studying properties of quantum channels acting on an n-partite system, whose action is invariant under permutations of the subsystems. Our main result is that, in order to prove that a certain property holds for any arbitrary input, it is sufficient to consider the special case where the input is a particular de Finetti-type state, i.e., a state which consists of n identical and independent copies of an (unknown) state on a single subsystem. Our method can be applied to the analysis of information-theoretic problems. For example, in quantum cryptography, we get a simple proof for the fact that security of a discrete-variable quantum key distribution protocol against collective attacks implies security of the protocol against the most general attacks. The resulting security bounds are tighter than previously known bounds obtained by proofs relying on the exponential de Finetti theorem. We note that our results can be generalised to quantum channels that commute with the action of an arbitrary finite or compact group.

Thursday, 21 August 2008, at 3.30 p.m.

Dr. Parsa Bonderson,

Microsoft Station Q

Abstract:

The topological approach to quantum computing derives intrinsic fault-tolerance by encoding qubits in the non-local state spaces of non-Abelian anyons. The original prescription required topological charge measurement for qubit readout, and used braiding exchanges of anyons to execute computational gates. We present an anyonic analog of quantum state teleportation, and use it to show how a series of topological charge measurements may replace the physical transportation of computational anyons in the implementation of computational gates.

Microsoft Station Q

Abstract:

The topological approach to quantum computing derives intrinsic fault-tolerance by encoding qubits in the non-local state spaces of non-Abelian anyons. The original prescription required topological charge measurement for qubit readout, and used braiding exchanges of anyons to execute computational gates. We present an anyonic analog of quantum state teleportation, and use it to show how a series of topological charge measurements may replace the physical transportation of computational anyons in the implementation of computational gates.

Tuesday, 29 July 2008, at 3.30 p.m.

Wally Greenberg

(University of Maryland)

Abstract:

This will be an informal talk.

(University of Maryland)

Abstract:

This will be an informal talk.

Tuesday, 24 June 2008, at 11.00 a.m.

Vitaly Tarasov

(Steklov Institute of Mathematics, Indiana University-Purdue University Indianapolis)

Abstract:

I will discuss the relation between the algebraic Bethe ansatz for quantum integrable models and Schubert calculus in algebraic geometry discovered in the last five years. This relation turns out to be important and fruitful in both directions. The remarkable consequence is the completeness of the Bethe ansatz for the Gaudin model associated with the Lie algebra $gl_N$ and for the XXX spin-1/2 Heisenberg model.

(Steklov Institute of Mathematics, Indiana University-Purdue University Indianapolis)

Abstract:

I will discuss the relation between the algebraic Bethe ansatz for quantum integrable models and Schubert calculus in algebraic geometry discovered in the last five years. This relation turns out to be important and fruitful in both directions. The remarkable consequence is the completeness of the Bethe ansatz for the Gaudin model associated with the Lie algebra $gl_N$ and for the XXX spin-1/2 Heisenberg model.

Thursday, 12 June 2008, at 3.30 p.m.

T. R. Govindarajan

(Institute of Mathematical Sciences Chennai, India)

Abstract:

Gauge theories on Moyal (\theta_{\mu,\nu}) space time are introduced preserving twisted Poincare invariance. Spontaneous symmetry breakdown and issues in Higgs_{\theta} mechanism are exposed. Attempts towards standard model_{\theta} are pointed out.

(Institute of Mathematical Sciences Chennai, India)

Abstract:

Gauge theories on Moyal (\theta_{\mu,\nu}) space time are introduced preserving twisted Poincare invariance. Spontaneous symmetry breakdown and issues in Higgs_{\theta} mechanism are exposed. Attempts towards standard model_{\theta} are pointed out.

Thursday, 5 June 2008, at 3.30 p.m.

Peter Schupp

(Jacobs University Bremen)

Abstract:

At length scales where both gravitational and quantum effects are important, the classical picture of smooth commutative spacetime should be replaced by some kind of quantum geometry. Motivated by this idea much research has been devoted to the study of quantum field theory on noncommutative spacetimes. In recent years one focus of research on non-commutative spaces has started shift to gravity, i.e. back to the motivating origins. In the talk we discuss the formulation of general relativity on noncommutative spacetime and explore the possibility of exact solutions. A fuzzy Schwarzschild-type solution is found with a discrete "quantum" spacetime that quite naturally exhibits holographic behavior.

(Jacobs University Bremen)

Abstract:

At length scales where both gravitational and quantum effects are important, the classical picture of smooth commutative spacetime should be replaced by some kind of quantum geometry. Motivated by this idea much research has been devoted to the study of quantum field theory on noncommutative spacetimes. In recent years one focus of research on non-commutative spaces has started shift to gravity, i.e. back to the motivating origins. In the talk we discuss the formulation of general relativity on noncommutative spacetime and explore the possibility of exact solutions. A fuzzy Schwarzschild-type solution is found with a discrete "quantum" spacetime that quite naturally exhibits holographic behavior.

Thursday, 29 May 2008, at 3.30 p.m.

Kumar Gupta

(Saha Institute of Nuclear Physics, Kolkata, India)

Abstract:

The analysis of quasi-normal modes of black holes provides a tool to probe the underlying geometry. In this talk we shall explore the connection between the quasi-normal modes and holography. We shall show that the quasi-normal modes of the BTZ black hole follows from the Sullivan's theorem, which encodes a precise mathematical statement for holography for the BTZ. A possible route towards non-commutative holography would also be explored.

(Saha Institute of Nuclear Physics, Kolkata, India)

Abstract:

The analysis of quasi-normal modes of black holes provides a tool to probe the underlying geometry. In this talk we shall explore the connection between the quasi-normal modes and holography. We shall show that the quasi-normal modes of the BTZ black hole follows from the Sullivan's theorem, which encodes a precise mathematical statement for holography for the BTZ. A possible route towards non-commutative holography would also be explored.

Thursday, 22 May 2008, at 3.30 p.m.

Paul Fendley

(University of Virginia, Charlottesville / Oxford)

Abstract:

I explain how the entanglement entropy of both the gapped bulk excitations and the gapless edge modes in a 2+1 dimensional topological phase can be encoded in a single partition function. This partition function is holographic because it can be expressed entirely in terms of the conformal field theory describing the edge modes. Examples include abelian and non-abelian fractional quantum Hall states, and p+ip superconductors. Including a point contact allows tunneling between two points on the edge, causing thermodynamic entropy to be lost with decreasing temperature. Such a perturbation effectively breaks the system in two, and the thermodynamic entropy loss is the same as that of the edge entanglement entropy. The non-integer `ground state degeneracy' obtained in 1+1-dimensional quantum impurity problems then has a nice interpretation: its logarithm is a 2+1-dimensional topological entanglement entropy.

(University of Virginia, Charlottesville / Oxford)

Abstract:

I explain how the entanglement entropy of both the gapped bulk excitations and the gapless edge modes in a 2+1 dimensional topological phase can be encoded in a single partition function. This partition function is holographic because it can be expressed entirely in terms of the conformal field theory describing the edge modes. Examples include abelian and non-abelian fractional quantum Hall states, and p+ip superconductors. Including a point contact allows tunneling between two points on the edge, causing thermodynamic entropy to be lost with decreasing temperature. Such a perturbation effectively breaks the system in two, and the thermodynamic entropy loss is the same as that of the edge entanglement entropy. The non-integer `ground state degeneracy' obtained in 1+1-dimensional quantum impurity problems then has a nice interpretation: its logarithm is a 2+1-dimensional topological entanglement entropy.

Thursday, 15 May 2008, at 3.30 p.m.

Simon Trebst

(Microsoft Research)

Abstract:

Topological quantum liquids in two dimensions such as the fractional quantum Hall states harbor exotic quasiparticles which due to their unusual exchange statistics are referred to as anyons. In this talk I will discuss the rich physics arising in one-dimensional models of interacting anyons, and highlight some of our results in the context of both two-dimensional classical systems and one-dimensional quantum spin systems. In particular, I will introduce generalizations of quantum spin Hamiltonians to anyonic degrees of freedom, such as the Heisenberg model or the Majumdar-Ghosh Hamiltonian. For chains of interacting Fibonacci anyons the energetic competition of two- and three-anyon interactions gives rise to a rich phase diagram with multiple critical and gapped phases. For the critical phases and their endpoints I will use numerical results to establish descriptions in terms of two-dimensional conformal field theory, and shortly discuss exact analytical results. I will then highlight the role of an inherent topological symmetry in protecting the critical phases. Finally, I will address how some of these findings generalize to other species of non-Abelian anyons.

(Microsoft Research)

Abstract:

Topological quantum liquids in two dimensions such as the fractional quantum Hall states harbor exotic quasiparticles which due to their unusual exchange statistics are referred to as anyons. In this talk I will discuss the rich physics arising in one-dimensional models of interacting anyons, and highlight some of our results in the context of both two-dimensional classical systems and one-dimensional quantum spin systems. In particular, I will introduce generalizations of quantum spin Hamiltonians to anyonic degrees of freedom, such as the Heisenberg model or the Majumdar-Ghosh Hamiltonian. For chains of interacting Fibonacci anyons the energetic competition of two- and three-anyon interactions gives rise to a rich phase diagram with multiple critical and gapped phases. For the critical phases and their endpoints I will use numerical results to establish descriptions in terms of two-dimensional conformal field theory, and shortly discuss exact analytical results. I will then highlight the role of an inherent topological symmetry in protecting the critical phases. Finally, I will address how some of these findings generalize to other species of non-Abelian anyons.

Thursday, 8 May 2008, at 3.30 p.m.

Charles Young

(Durham)

Abstract:

There exists a family of deformations of Minkowski spacetime, and its Poincare symmetries, parameterized by a mass-scale kappa. Understanding kappa-deformed quantum field theory poses an interesting challenge. I will discuss some recent work on one aspect of the problem: defining particle-exchange, and hence identical particles, in a kappa-covariant fashion.

(Durham)

Abstract:

There exists a family of deformations of Minkowski spacetime, and its Poincare symmetries, parameterized by a mass-scale kappa. Understanding kappa-deformed quantum field theory poses an interesting challenge. I will discuss some recent work on one aspect of the problem: defining particle-exchange, and hence identical particles, in a kappa-covariant fashion.

Wednesday, 23 April 2008, at 7.30 p.m.

With generous donation from Raymond Russell and Corvil Networks

Cryogenic Turbulence

K.R. Sreenivasan

(ICTP, Trieste)

Abstract:

SUPERFLUID LIQUID HELIUM exhibits quantum mechanical behaviour on a laboratory scale; like the energy levels of an atom, the angular momentum of vortices in a superfluid is quantized. This gives turbulence in liquid helium some strange particle-like behaviour and this quantized turbulence is very interesting, not least as a window into classical turbulence itself.

Location: Schroedinger LT, Fitzgerald Bldg, TCD

(ICTP, Trieste)

Abstract:

SUPERFLUID LIQUID HELIUM exhibits quantum mechanical behaviour on a laboratory scale; like the energy levels of an atom, the angular momentum of vortices in a superfluid is quantized. This gives turbulence in liquid helium some strange particle-like behaviour and this quantized turbulence is very interesting, not least as a window into classical turbulence itself.

Location: Schroedinger LT, Fitzgerald Bldg, TCD

Thursday, 17 April 2008, at 3.30 p.m.

James Lucietti

(Durham)

Abstract:

Extremal (especially BPS) black holes are of special importance in string theory and AdS/CFT. Their near-horizon geometries provide a precise tool for investigating such black holes. After reviewing certain aspects of higher dimensional black holes, I will discuss near-horizon geometries from a general point of view. I will then describe some specific applications of these ideas which will include: a classification of near-horizon geometries of asymptotically AdS(5) supersymmetric black holes with two rotational symmetries (of relevance to AdS/CFT), symmetry enhancement of generic near-horizon geometries in D=4,5 (of relevance to the attractor mechanism), near-horizon geometries in D>5 and finally some open problems.

(Durham)

Abstract:

Extremal (especially BPS) black holes are of special importance in string theory and AdS/CFT. Their near-horizon geometries provide a precise tool for investigating such black holes. After reviewing certain aspects of higher dimensional black holes, I will discuss near-horizon geometries from a general point of view. I will then describe some specific applications of these ideas which will include: a classification of near-horizon geometries of asymptotically AdS(5) supersymmetric black holes with two rotational symmetries (of relevance to AdS/CFT), symmetry enhancement of generic near-horizon geometries in D=4,5 (of relevance to the attractor mechanism), near-horizon geometries in D>5 and finally some open problems.

Thursday, 27 March 2008, at 3.30 p.m.

Nicolas Boulanger

(Scuola Normale Superiore)

Abstract:

The general solutions of the Wess-Zumino consistency condition for the conformal (or Weyl, or trace) anomalies are derived. The solutions are obtained, in arbitrary dimensions, by explicitly computing the cohomology of the corresponding Becchi-Rouet-Stora-Tyutin differential in the space of integrated local functions at ghost number unity. This provides a purely algebraic, regularization-independent classification of the Weyl anomalies in arbitrary dimensions. The so-called type-A anomaly is shown to satisfy a non-trivial descent of equations, similarly to the non-Abelian chiral anomaly in Yang-Mills theory.

(Scuola Normale Superiore)

Abstract:

The general solutions of the Wess-Zumino consistency condition for the conformal (or Weyl, or trace) anomalies are derived. The solutions are obtained, in arbitrary dimensions, by explicitly computing the cohomology of the corresponding Becchi-Rouet-Stora-Tyutin differential in the space of integrated local functions at ghost number unity. This provides a purely algebraic, regularization-independent classification of the Weyl anomalies in arbitrary dimensions. The so-called type-A anomaly is shown to satisfy a non-trivial descent of equations, similarly to the non-Abelian chiral anomaly in Yang-Mills theory.

Wednesday, 26 March 2008, at 3.30 p.m.

Nicolas Regnault

(Ecole Normale Superieure)

Abstract:

Role of spin-like internal degrees of freedom in the fractional quantum Hall regime has been intensively studied. This question has been addressed both for the "real" spin of electrons or the layer index in the case of bilayer systems. Recently, new physical systems such as graphene, have motivated a deeper look at richer internal degrees of freedom.

(Ecole Normale Superieure)

Abstract:

Role of spin-like internal degrees of freedom in the fractional quantum Hall regime has been intensively studied. This question has been addressed both for the "real" spin of electrons or the layer index in the case of bilayer systems. Recently, new physical systems such as graphene, have motivated a deeper look at richer internal degrees of freedom.

We will present the different strategies that have been developed to study this new cases. We will mainly focus on the generalized Halperin wave functions since there are a straightforward generalization of the Laughlin state. Even within this simple picture, we will show larger symmetry groups open new perspectives in the fractional quantum Hall physics.

Thursday, 28 February 2008, at 3.30 p.m.

Eddy Ardonne

(Nordita)

Abstract:

After giving an overview of some basics about the quantum Hall effect, I will motivate the study of so-called non-abelian quantum Hall states, via some (recent) experimental results, and the possible application of such states to quantum computation. The non-abelian statistics of the quantum Hall states we consider can be explained in an elementary fashion in an exactly solvable limit, namely the thin-torus limit. In this limit, the excitation are domain walls between various `ground states', and these domain walls give rise to the non-abelian statistics in a simple way. I will briefly discuss the connection the domain walls and conformal field theory (note that no knowledge of conformal field theory will be assumed).

(Nordita)

Abstract:

After giving an overview of some basics about the quantum Hall effect, I will motivate the study of so-called non-abelian quantum Hall states, via some (recent) experimental results, and the possible application of such states to quantum computation. The non-abelian statistics of the quantum Hall states we consider can be explained in an elementary fashion in an exactly solvable limit, namely the thin-torus limit. In this limit, the excitation are domain walls between various `ground states', and these domain walls give rise to the non-abelian statistics in a simple way. I will briefly discuss the connection the domain walls and conformal field theory (note that no knowledge of conformal field theory will be assumed).

Friday, 22 February 2008, at 3.30 p.m.

Jean Pierre Gazeau

(Paris 7)

Abstract:

A construction of the 2d and 4d fuzzy de Sitter hyperboloids is carried out by using a (vector) coherent state quantization. We get a natural discretization of the dS ``time " axis based on the spectrum of Casimir operators of the respective maximal compact su bgroups SO (2) and SO(4) of the de Sitter groups SO(1,2) and SO(1,4). The continuous limit at infinite spins is examined.

(Paris 7)

Abstract:

A construction of the 2d and 4d fuzzy de Sitter hyperboloids is carried out by using a (vector) coherent state quantization. We get a natural discretization of the dS ``time " axis based on the spectrum of Casimir operators of the respective maximal compact su bgroups SO (2) and SO(4) of the de Sitter groups SO(1,2) and SO(1,4). The continuous limit at infinite spins is examined.

Thursday, 7 February 2008, at 3.30 p.m.

Jose Gaite

(Instituto de Microgravedad, Univ. Politecnica de Madrid)

Abstract:

The large-scale structure of matter appears to be fractal over a range of scales. This is evidenced by observations of the distribution of galaxies and by numerical simulations of dark matter models. In addition, the theoretical description of cosmic structure formation with the methods of non-equilibrium statistical mechanics leads to scaling laws and, in particular, to the dynamical scaling hypothesis. We review the Zeldovich approximation and the adhesion model, which predict the observed structure (the "cosmic web"). The adhesion model can be studied with the methods of perturbation theory and the renormalization group. However, these methods are only successful in one dimension, whereas the three-dimensional case requires non-perturbative methods. Therefore, we introduce coarse-graining approaches and, in particular, the exact renormalization group, which are of general application in the dynamics of structure formation.

(Instituto de Microgravedad, Univ. Politecnica de Madrid)

Abstract:

The large-scale structure of matter appears to be fractal over a range of scales. This is evidenced by observations of the distribution of galaxies and by numerical simulations of dark matter models. In addition, the theoretical description of cosmic structure formation with the methods of non-equilibrium statistical mechanics leads to scaling laws and, in particular, to the dynamical scaling hypothesis. We review the Zeldovich approximation and the adhesion model, which predict the observed structure (the "cosmic web"). The adhesion model can be studied with the methods of perturbation theory and the renormalization group. However, these methods are only successful in one dimension, whereas the three-dimensional case requires non-perturbative methods. Therefore, we introduce coarse-graining approaches and, in particular, the exact renormalization group, which are of general application in the dynamics of structure formation.

Monday, 17 December 2007, at 3.30 p.m.

Jemal Guven

(University of Mexico)

Abstract:

A variational framework is introduced to describe how a surface bends when it is subject to local constraints on its geometry. This framework is applied to describe the patterns observed in a folded sheet of paper. The unstretchability of paper implies a constraint on the surface metric; bending is penalized by an energy quadratic in mean curvature. The local Lagrange multipliers enforcing the constraint are identified with a conserved tangential stress that couples to the extrinsic curvature of the sheet. The framework is illustrated by examining the deformation of a flat sheet into a generalized cone.

(University of Mexico)

Abstract:

A variational framework is introduced to describe how a surface bends when it is subject to local constraints on its geometry. This framework is applied to describe the patterns observed in a folded sheet of paper. The unstretchability of paper implies a constraint on the surface metric; bending is penalized by an energy quadratic in mean curvature. The local Lagrange multipliers enforcing the constraint are identified with a conserved tangential stress that couples to the extrinsic curvature of the sheet. The framework is illustrated by examining the deformation of a flat sheet into a generalized cone.

Thursday, 6 December 2007, at 3.30 p.m.

Jon Shock

(Santiago de Compostela)

Abstract:

(Santiago de Compostela)

Abstract:

Thursday, 29 November 2007, at 3.30 p.m.

Joerg Teschner

(DESY)

Abstract:

We will describe our recent work, partially joint with A. Bytsko on the spectrum of the Sinh-Gordon model. It is based on an integrable lattice regularization which has a quantum group structure related to the modular double. Algebraic Bethe ansatz fails in this case, but the construction of the Q-operator combined with the Separation of Variables Method lead to a complete characterization of the spectrum in terms of a certain set of solution to the Baxter equation. Building on these results we will describe how to reformulate this description of the spectrum in terms of nonlinear integral equations and how to take the continuum limit. A conjecture is formulated concerning the uniqueness of the solutions to the resulting integral equations. This conjecture passes nontrivial checks in the semiclassical, the infrared and the ultraviolet limits, respectively. We observe in particular highly nontrivial relations to Liouville theory.

(DESY)

Abstract:

We will describe our recent work, partially joint with A. Bytsko on the spectrum of the Sinh-Gordon model. It is based on an integrable lattice regularization which has a quantum group structure related to the modular double. Algebraic Bethe ansatz fails in this case, but the construction of the Q-operator combined with the Separation of Variables Method lead to a complete characterization of the spectrum in terms of a certain set of solution to the Baxter equation. Building on these results we will describe how to reformulate this description of the spectrum in terms of nonlinear integral equations and how to take the continuum limit. A conjecture is formulated concerning the uniqueness of the solutions to the resulting integral equations. This conjecture passes nontrivial checks in the semiclassical, the infrared and the ultraviolet limits, respectively. We observe in particular highly nontrivial relations to Liouville theory.

Thursday, 23 November 2007, at 3.30 p.m.

Yusuke Kimura

(Queen Mary College)

Abstract:

I will propose gauge theory operators built using a complex Matrix scalar which are dual to brane-anti-brane systems in AdS_5 \times S^5, in the zero coupling limit of the dual Yang-Mills. The branes involved are half-BPS giant gravitons. The proposed operators dual to giant-anti-giant configurations satisfy the appropriate orthogonality properties.Projection operators in Brauer algebras are used to construct the relevant multi-trace Matrix operators. The reference is arXiv:0709.2158, which is based on work with S. Ramgoolam (QMUL).

(Queen Mary College)

Abstract:

I will propose gauge theory operators built using a complex Matrix scalar which are dual to brane-anti-brane systems in AdS_5 \times S^5, in the zero coupling limit of the dual Yang-Mills. The branes involved are half-BPS giant gravitons. The proposed operators dual to giant-anti-giant configurations satisfy the appropriate orthogonality properties.Projection operators in Brauer algebras are used to construct the relevant multi-trace Matrix operators. The reference is arXiv:0709.2158, which is based on work with S. Ramgoolam (QMUL).

Tuesday, 16 October 2007, at 3.30 p.m.

Jiannis Pachos

(Leeds U.)

Abstract:

At half filling, the electronic structure of graphene can be modeled by a pair of two-dimensional Weyl fermions. The introduction of curvature couples these fermions to a chiral gauge field. The further introduction of a Kekule structure couples them to a mass-generating Higgs field. In the presence of the geometrically induced gauge field, an everywhere-real Kekule modulation of the hopping matrix elements can correspond to a non-real Higgs field with non-trivial vorticity. For the case of fullerenes, that is spherical configurations of graphene, an index theorem allows for the existence of six low-lying modes. The related fresh reference is arXiv:0710.0858.

(Leeds U.)

Abstract:

At half filling, the electronic structure of graphene can be modeled by a pair of two-dimensional Weyl fermions. The introduction of curvature couples these fermions to a chiral gauge field. The further introduction of a Kekule structure couples them to a mass-generating Higgs field. In the presence of the geometrically induced gauge field, an everywhere-real Kekule modulation of the hopping matrix elements can correspond to a non-real Higgs field with non-trivial vorticity. For the case of fullerenes, that is spherical configurations of graphene, an index theorem allows for the existence of six low-lying modes. The related fresh reference is arXiv:0710.0858.

Friday, 12 October 2007, at 3.30 p.m.

Martin Crocce

(Institut de Ciencies de l'Espai)

Abstract:

I will present a new approach to study the nonlinear evolution in the growth of large-scale structure by following the dynamics of gravitational clustering as it builds up in time. This approach, based on Feynman diagrammatic and re-summation techniques, solves fundamental problems in the description of density perturbations and provides a powerful technique to model accurately their transition to the nonlinear regime. I will show concrete practical applications at the two-point statistics level (e.g. Baryon Acoustic Oscillations), as well as sketch extensions to higher order ones.

(Institut de Ciencies de l'Espai)

Abstract:

I will present a new approach to study the nonlinear evolution in the growth of large-scale structure by following the dynamics of gravitational clustering as it builds up in time. This approach, based on Feynman diagrammatic and re-summation techniques, solves fundamental problems in the description of density perturbations and provides a powerful technique to model accurately their transition to the nonlinear regime. I will show concrete practical applications at the two-point statistics level (e.g. Baryon Acoustic Oscillations), as well as sketch extensions to higher order ones.

Thursday, 27 September 2007, at 3.30 p.m.

Nikolas Akerblom

(Max-Planck-Institut fuer Physik, Muenchen)

Abstract:

Recent times have seen embiggened interest in D-instanton effects in intersecting D-brane models. In this talk we highlight two particular results in this direction. First, we discuss the derivation of the Affleck-Dine-Seiberg superpotential from E2-branes. Second, we consider the effect such euclidean branes might have on holomorphic quantities in the low-energy effective action, such as the gauge kinetic function.

(Max-Planck-Institut fuer Physik, Muenchen)

Abstract:

Recent times have seen embiggened interest in D-instanton effects in intersecting D-brane models. In this talk we highlight two particular results in this direction. First, we discuss the derivation of the Affleck-Dine-Seiberg superpotential from E2-branes. Second, we consider the effect such euclidean branes might have on holomorphic quantities in the low-energy effective action, such as the gauge kinetic function.

Tuesday, 25 September 2007, at 3.30 p.m.

Kazuhiko Nishijima

(Helsinki)

(Helsinki)

Tuesday, 11 September 2007, at 7.00 p.m.

Michael Freedman

(Microsoft Research, Station Q, Santa Barbara)

Abstract:

Since Milnor found the exotic 7-spheres in 1956, gluing has played a key role in topology. In this talk, I will consider gluing of superpositions of manifolds. It turns out that there is a dramatic difference according to dimension. The natural pairings induced by gluing have null vectors when the manifold dimension is 4 or higher, in contrast the pairings are positive when the dimension is 3 or lower. I will explain the implications for quantum mechanics.

(Microsoft Research, Station Q, Santa Barbara)

Abstract:

Since Milnor found the exotic 7-spheres in 1956, gluing has played a key role in topology. In this talk, I will consider gluing of superpositions of manifolds. It turns out that there is a dramatic difference according to dimension. The natural pairings induced by gluing have null vectors when the manifold dimension is 4 or higher, in contrast the pairings are positive when the dimension is 3 or lower. I will explain the implications for quantum mechanics.

Thursday, 6 September 2007, at 4.00 p.m.

Steve Simon

(Alcatel-Lucent, Bell Labs)

Abstract:

In the modern information era, where the demand for higher bit-rate seems to be increasing without bound, it is essential to understand the physical limits on communications. I will start by reviewing the concept of a Shannon limit of how many bits per second can be conveyed from a transmitter to a receiver. We then discover that in a disordered environment (in a city, for example) it becomes essential to understand wave interference in order to find this Shannon limit for modern communication systems. It becomes advantageous to make an analogy between radio waves in cities and electron waves in disordered metals. Using our understanding of mesoscopics we can understand more about howinformation capacity is limited. We find the question of information can be reduced to a random matrix problem which is attacked with traditional condensed matter field theory methods. Finally we bring the story full-circle by deducing new insights about mesoscopics from our results on wireless communications.

(Alcatel-Lucent, Bell Labs)

Abstract:

In the modern information era, where the demand for higher bit-rate seems to be increasing without bound, it is essential to understand the physical limits on communications. I will start by reviewing the concept of a Shannon limit of how many bits per second can be conveyed from a transmitter to a receiver. We then discover that in a disordered environment (in a city, for example) it becomes essential to understand wave interference in order to find this Shannon limit for modern communication systems. It becomes advantageous to make an analogy between radio waves in cities and electron waves in disordered metals. Using our understanding of mesoscopics we can understand more about howinformation capacity is limited. We find the question of information can be reduced to a random matrix problem which is attacked with traditional condensed matter field theory methods. Finally we bring the story full-circle by deducing new insights about mesoscopics from our results on wireless communications.

Wednesday, 27 June 2007, at 3.30 p.m.

Thomas Curtright

(University of Miami)

Abstract:

I will briefly discuss properties of quasi-hermitian (PT-symmetric) theories in the context of a simple exactly solvable example, imaginary Liouville theory. I will use a deformation quantization approach, i.e. QM in phase space. Then I will discuss the field theory extension of this model, of interest in string theory.

(University of Miami)

Abstract:

I will briefly discuss properties of quasi-hermitian (PT-symmetric) theories in the context of a simple exactly solvable example, imaginary Liouville theory. I will use a deformation quantization approach, i.e. QM in phase space. Then I will discuss the field theory extension of this model, of interest in string theory.

Thursday, 03 May 2007, at 4.30 p.m.

Eliezer Rabinovici

(The Hebrew University)

Abstract:

We discuss the issue of a Hagedorn spectrum in Little String Theory.

(The Hebrew University)

Abstract:

We discuss the issue of a Hagedorn spectrum in Little String Theory.

Wednesday, 02 May 2007, at 3.30 p.m.

Yuri Suhov

(University of Cambridge)

Abstract:

I will review a recent paper by Kontsevich and myself under the same title. See math-ph/0609056.

(University of Cambridge)

Abstract:

I will review a recent paper by Kontsevich and myself under the same title. See math-ph/0609056.

Thursday, 19 April 2007, at 3.30 p.m.

Martin Wolf

(Imperial College, London)

Abstract:

In this talk, I will discuss certain aspects of integrability in supersymmetric Yang-Mills (SYM) theories. I first give a brief review about twistor theory and then discuss the construction of nonlocal symmetry algebras in self-dual and non-self-dual SYM theories. In particular, in the case of the maximally SYM theory, I describe the construction of an infinite sequence of flows on the solution space of the N=4 SYM equations based on a generalization of the supertwistor correspondence. The N=4 SYM equations are embedded into the infinite system of the hierarchy equations and in addition this SYM hierarchy is associated with an infinite set of graded symmetries recursively generated from supertranslations.

(Imperial College, London)

Abstract:

In this talk, I will discuss certain aspects of integrability in supersymmetric Yang-Mills (SYM) theories. I first give a brief review about twistor theory and then discuss the construction of nonlocal symmetry algebras in self-dual and non-self-dual SYM theories. In particular, in the case of the maximally SYM theory, I describe the construction of an infinite sequence of flows on the solution space of the N=4 SYM equations based on a generalization of the supertwistor correspondence. The N=4 SYM equations are embedded into the infinite system of the hierarchy equations and in addition this SYM hierarchy is associated with an infinite set of graded symmetries recursively generated from supertranslations.

Thursday, 29 March 2007, at 3.30 p.m.

Maxim Samsonov

(Dublin Institute for Advanced Studies)

Abstract:

I consider the problem of explicit construction of affine Drinfeld twists for U_q(sl[u]) and their Yangian analogues. The method itself is based on proposing an ansatz formula for affine twists in the form close to coboundary twist. It can be shown that many bialgebraic structures on polynomial current algebras corresponding to the solutions of the rational Yang-Baxter equation allow quantisation and can be treated as quasi-classical limits of the Hopf algebra structures on the twist-deformed quantum affine enveloping algebra.

(Dublin Institute for Advanced Studies)

Abstract:

I consider the problem of explicit construction of affine Drinfeld twists for U_q(sl[u]) and their Yangian analogues. The method itself is based on proposing an ansatz formula for affine twists in the form close to coboundary twist. It can be shown that many bialgebraic structures on polynomial current algebras corresponding to the solutions of the rational Yang-Baxter equation allow quantisation and can be treated as quasi-classical limits of the Hopf algebra structures on the twist-deformed quantum affine enveloping algebra.

Thursday, 15 March 2007, at 3.30 p.m.

David Rideout

(Imperial College, London)

Abstract:

The various entropy bounds that exist in the literature suggest that spacetime is fundamentally discrete, and hint at an underlying relationship between geometry and ``information''. The foundation of this relationship is yet to be uncovered, but should manifest itself in a theory of quantum gravity. We present a measure for the maximal entropy of spherically symmetric spacelike regions within the causal set approach to quantum gravity. In terms of the proposal, a bound for the entropy contained in this region can be derived from a counting of potential ``degrees of freedom'' associated to the Cauchy horizon of its future domain of dependence. For different spherically symmetric spacelike regions in Minkowski spacetime of arbitrary dimension, we show that this proposal leads, in the continuum approximation, to Susskind's well-known spherical entropy bound.

PDF-File

(Imperial College, London)

Abstract:

The various entropy bounds that exist in the literature suggest that spacetime is fundamentally discrete, and hint at an underlying relationship between geometry and ``information''. The foundation of this relationship is yet to be uncovered, but should manifest itself in a theory of quantum gravity. We present a measure for the maximal entropy of spherically symmetric spacelike regions within the causal set approach to quantum gravity. In terms of the proposal, a bound for the entropy contained in this region can be derived from a counting of potential ``degrees of freedom'' associated to the Cauchy horizon of its future domain of dependence. For different spherically symmetric spacelike regions in Minkowski spacetime of arbitrary dimension, we show that this proposal leads, in the continuum approximation, to Susskind's well-known spherical entropy bound.

PDF-File

Thursday, 8 March 2007, at 3.30 p.m.

Matthias Ihl

(University of Texas at Austin)

Abstract:

I will try to describe some of the experimental evidence that leads us to believe that the fireball produced in Au-Au colissions at RHIC is a rapidly thermalizing, strongly-coupled Quark-Gluon-Plasma (sQGP). I will also motivate why and to what extent AdS/CFT can be hoped to provide a theoretical tool to study the sQGP. To this end, some progress has been made in N=1 SQCD-like theories, i.e. theories with dynamical quarks.

PDF-File

(University of Texas at Austin)

Abstract:

I will try to describe some of the experimental evidence that leads us to believe that the fireball produced in Au-Au colissions at RHIC is a rapidly thermalizing, strongly-coupled Quark-Gluon-Plasma (sQGP). I will also motivate why and to what extent AdS/CFT can be hoped to provide a theoretical tool to study the sQGP. To this end, some progress has been made in N=1 SQCD-like theories, i.e. theories with dynamical quarks.

PDF-File

Thursday, 1 March 2007, at 3.30 p.m.

Bernard Julia

(Ecole Normale Superieure, Paris)

(Ecole Normale Superieure, Paris)

Thursday, 22 February 2007, at 3.30 p.m.

Nemani Suryanarayana

(Imperial College, London)

Abstract:

Accounting for the entropy of the supersymmetric black holes in AdS(5) remains an open problem. In this talk I will describe a (promising) new approach to address this problem which is to count an appropriate set of BPS D-branes in the near horizon geometry of the black hole.

(Imperial College, London)

Abstract:

Accounting for the entropy of the supersymmetric black holes in AdS(5) remains an open problem. In this talk I will describe a (promising) new approach to address this problem which is to count an appropriate set of BPS D-branes in the near horizon geometry of the black hole.

Thursday, 15 February 2007, at 3.30 p.m.

Yang-Hui He

(Oxford)

Abstract:

We study gauge theories which arise from D-branes on Calabi-Yau spaces and advocate a ``Plethystic Programme'' which provides a simple bridge between (1) the defining equation of the Calabi-Yau, (2) the generating function of single-trace BPS operators and (3) the generating function of multi-trace operators. Mathematically, fascinating and intricate inter-relations between quiver theories, algebraic geometry and combinatorics exhibit themselves in the form of plethystics and syzygies.

PDF-File

(Oxford)

Abstract:

We study gauge theories which arise from D-branes on Calabi-Yau spaces and advocate a ``Plethystic Programme'' which provides a simple bridge between (1) the defining equation of the Calabi-Yau, (2) the generating function of single-trace BPS operators and (3) the generating function of multi-trace operators. Mathematically, fascinating and intricate inter-relations between quiver theories, algebraic geometry and combinatorics exhibit themselves in the form of plethystics and syzygies.

PDF-File

Thursday, 8 February 2007, at 3.30 p.m.

James Gray

(Institut d'Astrophysique de Paris)

Abstract:

I will discuss the derivation of the perturbative four-dimensional effective theory describing heterotic M-theory with branes and anti-branes in the bulk space. The back-reaction of both the branes and anti-branes will be explicitly included.

To first order in the heterotic strong-coupling expansion, we will find that the forces on branes and anti-branes vanish and that the 'KKLT' procedure of simply adding to the supersymmetric theory the probe approximation to the energy density of the anti-brane reproduces the correct potential.

However, there are additional non-supersymmetric corrections to the gauge-kinetic functions and matter terms. The new correction to the gauge kinetic functions is important in a discussion of moduli stabilization. At second order in the strong-coupling expansion, we will find that the forces on the branes and anti-branes become non-vanishing. These forces are not precisely in the naive form that one may have anticipated and, being second order in the small parameter of the strong-coupling expansion, they are relatively weak. This suggests that moduli stabilization in heterotic models with anti-branes is achievable

(Institut d'Astrophysique de Paris)

Abstract:

I will discuss the derivation of the perturbative four-dimensional effective theory describing heterotic M-theory with branes and anti-branes in the bulk space. The back-reaction of both the branes and anti-branes will be explicitly included.

To first order in the heterotic strong-coupling expansion, we will find that the forces on branes and anti-branes vanish and that the 'KKLT' procedure of simply adding to the supersymmetric theory the probe approximation to the energy density of the anti-brane reproduces the correct potential.

However, there are additional non-supersymmetric corrections to the gauge-kinetic functions and matter terms. The new correction to the gauge kinetic functions is important in a discussion of moduli stabilization. At second order in the strong-coupling expansion, we will find that the forces on the branes and anti-branes become non-vanishing. These forces are not precisely in the naive form that one may have anticipated and, being second order in the small parameter of the strong-coupling expansion, they are relatively weak. This suggests that moduli stabilization in heterotic models with anti-branes is achievable

Thursday, 1 February 2007, at 3.30 p.m.

Sebastian Uhlmann

(Universität Jena)

Abstract:

We outline several exemplary applications and classes of invariant group integrals in lattice gauge theory and derive two types of Ward identities for the generating functions for invariant integrals of monomials of the fundamental characters for arbitrary simple compact Lie groups. The results are applied to the groups SU(3), Spin(5) and G_2 of rank 2 as well as SU(4).

(Universität Jena)

Abstract:

We outline several exemplary applications and classes of invariant group integrals in lattice gauge theory and derive two types of Ward identities for the generating functions for invariant integrals of monomials of the fundamental characters for arbitrary simple compact Lie groups. The results are applied to the groups SU(3), Spin(5) and G_2 of rank 2 as well as SU(4).

Tuesday, 30 January 2007, at 12.15 p.m.

Michael Douglas

(Rutgers University)

(Rutgers University)

Thursday, 25 January 2007, at 3.30 p.m.

Harold Steinacker

(Universität Wien)

Abstract:

We present a new model for Yang-Mills theory on the fuzzy sphere in which the configuration space of gauge fields is given by a compact symplectic space. This allows to apply the technique of nonabelian localization resp. equivariant cohomology to compute the partition function, which is given exactly by a sum of saddle-point contributions. We evaluate these contributions explicitly for the generic case.

The known result for 2D Yang-Mills on the sphere is recovered in the commutative limit.

(Universität Wien)

Abstract:

We present a new model for Yang-Mills theory on the fuzzy sphere in which the configuration space of gauge fields is given by a compact symplectic space. This allows to apply the technique of nonabelian localization resp. equivariant cohomology to compute the partition function, which is given exactly by a sum of saddle-point contributions. We evaluate these contributions explicitly for the generic case.

The known result for 2D Yang-Mills on the sphere is recovered in the commutative limit.

Thursday, 18 January 2007, at 3.30 p.m.

Mikhail Volkov

(Universite de Tours)

Abstract:

Classical solutions describing strings endowed with an electric charge and carrying a constant electromagnetic current are constructed within the bosonic sector of the Electroweak Theory and also in the Einstein-Yang-Mills theory.

(Universite de Tours)

Abstract:

Classical solutions describing strings endowed with an electric charge and carrying a constant electromagnetic current are constructed within the bosonic sector of the Electroweak Theory and also in the Einstein-Yang-Mills theory.

Wednesday, 17 January 2007, at 3.30 p.m.

O.W. Greenberg

(Department of Physics, University of Maryland)

Abstract:

I will describe a composite model with exactly three generations of quarks and leptons. The observable consequences of this model include (1) heavy quarks and leptons that will have two-body decays with no missing energy, (2) a new scenario for the Higgs meson in which the Higgs decay rates are no longer connected to the quark masses, (3) reduction by a factor of three in the cross section for e^+ e^- to hadrons at high energy, and (4) a new candidate for dark matter. The standard model gauge bosons will not couple directly to the quarks and leptons, but instead will couple indirectly via one of the constituents.

(Department of Physics, University of Maryland)

Abstract:

I will describe a composite model with exactly three generations of quarks and leptons. The observable consequences of this model include (1) heavy quarks and leptons that will have two-body decays with no missing energy, (2) a new scenario for the Higgs meson in which the Higgs decay rates are no longer connected to the quark masses, (3) reduction by a factor of three in the cross section for e^+ e^- to hadrons at high energy, and (4) a new candidate for dark matter. The standard model gauge bosons will not couple directly to the quarks and leptons, but instead will couple indirectly via one of the constituents.