Tom Brown
(Queen Mary University, London)

Abstract:

We calculate transition probabilities for various processes involving giant gravitons and small gravitons in AdS space, using the dual N=4 SYM theory. The normalization factors for these probabilities involve, in general, correlators for manifolds of non-trivial topology which are obtained by gluing simpler four-manifolds. This follows from the factorization properties which relate CFT correlators for different topologies.  We give the bulk five dimensional interpretation, involving neighborhoods of Witten graphs, of these gluing properties of the four dimensional boundary CFT. As a corollary we give a simple description, based on Witten graphs, of a multiplicity of bulk topologies corresponding to a fixed boundary topology. We also propose to interpret the correlators as topology-changing transition amplitudes between LLM geometries.

Jemal Guven
(ICN UNAM, Mexico)

Neil O' Connell
(University College Cork)

Abstract:

I will discuss some interpretations and extensions of a measure which arises in random matrix theory via the Harish-Chandra (or Itzykson-Zuber) spherical integral formula, and in representation theory when one considers the asymptotics of multiplicities associated with irredicible representations of complex semi-simple Lie groups. In the latter context, it is known as the Duistermaat-Heckman measure. We show that this measure can be constructed directly in terms of the Weyl group via a Brownian path model, and that this construction extends to the more general setting of Coxeter groups. The Duistermaat-Heckman measure is known to be the push-forward, via a linear transformation, of Lebesgue measure on a certain convex polytope. We extend this result to the general case using the Brownian path model. This is joint work with Philippe Biane and Philippe Bougerol.

D. Leites
(Stockholm University)

Abstract:

The simple Lie algebras are nowadays described usually in terms of root systems. Eli Cartan used a totally different approach: he interpreted Lie algebras as preserving non-integrable distributions. In 1960s, Kostrikin and Shafarevich conjectured a description of simple finite dimensional Lie algebras over algebraically closed fields of characteristic p>7. Recently the amended conjecture had been proved for p>3 (Block-Wilson, Premet, Strade). Cartan's approach allowed Grozman and me elucidate several mysterious Lie algebras for p=3, and find two new series of simple algebras. I'll tell what we got up today using this approach in super setting. The most interesting to me in this activity is the realization of the fact that I do not understand what U(g) is for p>0. What bothers me concerns the notions of representations and deformations. Now, recall that the representations of quantum U_q(g) are supposed to resemble representations of Lie algebras in char. p>0. But if the notion of representation is unclear (as I claim), what are we talking about?

Andreas Winter
(University of Bristol)

Abstract:

We introduce a new state discrimination problem in which we are given additional information about the state after the measurement, or more generally, after a quantum memory bound applies. In particular, the following special case plays an important role in quantum cryptographic protocols in the bounded storage model: Given a string x encoded in an unknown basis chosen from a set of mutually unbiased bases, you may perform any measurement, but then store at most q qubits of quantum information. Later on, you learn which basis was used. How well can you compute a function f(x) of x, given the initial measurement outcome, the q qubits and the additional basis information? We first show a lower bound on the success probability for any balanced function, and any number of mutually unbiased bases, beating the naive strategy of simply guessing the basis. We then show that for two bases, any Boolean function f(x) can be computed perfectly if you are allowed to store just a single qubit, independent of the number of possible input strings x. However, we show how to construct three bases, such that you need to store all qubits in order to compute f(x) perfectly. We then investigate how much advantage the additional basis information can give for a Boolean function. To this end, we prove optimal bounds for the success probability for the AND and the XOR function for up to three mutually unbiased bases. Our result shows that the gap in success probability can be maximal: without the basis information, you can never do better than guessing the basis, but with this information, you can compute f(x) perfectly. We also exhibit an example where the extra information does not give any advantage at all.

related publications: [1]

Robbert Dijkgraaf
(Universiteit van Amsterdam)

Abstract:

Many exact solutions of 4d supersymmetric gauge theories can be formulated in terms of 2d free fermion systems. I will show how ideas from string theory naturally lead to such a description that connects instanton computations, conformal field theories, and integrable systems.

R. Manvelyan
(Technische Universität Kaiserslautern, Germany, and Yerevan Physics Institute, Armenia)

Abstract:

The hierarchy of conformally coupled scalars with the increasing scaling dimensions \Delta_{k}=k-d/2 , k=1,2,3,... connected with the k-th Euler density in the corresponding space time dimensions d\geq 2k is proposed. The corresponding conformal invariant Lagrangians with k-th power of Laplacian for the already known cases k=1,2 are reviewed and the subsequent case of k=3 is completely constructed and analyzed.

O.W. Greenberg
(University of Maryland, currently visitor at DIAS)

Abstract:

The model has exactly three generations of quarks and leptons at presently accessible energies. I will describe both the positive and the problematic features of the model. I will also give generic predictions of models of this type for energies much higher than are presently available, in particular two body decays with no missing energy. The model has an inert scalar particle that is a candidate for dark energy.

Rabin Banerjee
(S.N. Bose National Centre for Basic Sciences, Kolkata, India)

Abstract:

There are two ways of implementing gauge symmetries on a noncommutative space. Either gauge transformations are deformed while preserving the standard comultiplication (Leibniz) rule or gauge transformations are retained as in the commutative case at the price of giving up the Leibniz rule. Both these approaches will be discussed from a first principle analysis which also shows their connection with the usual treatment of gauge symmetries on commutative spaces.

R. Manvelyan
(Technische Universität Kaiserslautern, Germany, and Yerevan Physics Institute, Armenia)

Abstract:

related publications: [1] [2]

F. A. Dolan
(Cambridge University, UK)

O. J. Rosten
(University of Southampton, UK)

Abstract:

PDF-File

M. Chaichian
(University of Helsinki, Finland)

Abstract:

After a brief review of the field and the arguments for a noncommutative space-time, the twist-Poincaré symmetry and its implications will be discussed.

P. Majumdar
(Saha Institute of Nuclear Physics, Calcutta, India)

Abstract:

I shall begin with a review of Isolated Horizons as a non-stationary local generalization of stationary event horizons, and briefly discuss the degrees of freedom which describe its dynamics. Then, after a brief review of Loop Quantum Gravity, I'll describe an ab initio computation of the microcanonical entropy of isolated horizons for macroscopic horizon areas. Next I shall discuss non-isolated radiant black holes, and address the issue of such black holes being in stable thermal equilibrium with their radiation bath. A criterion for thermal stability will be derived from elementary statistical mechanical considerations, and without recourse to specific black hole metrics, in terms of quantities well-understood within the LQG treatment of isolated horizons. Additional thermal fluctuations induced corrections to the canonical entropy will also be touched upon.

B. Ydri
(Badji Mokhtar-Annaba University, Algeria)

Abstract:

We find using Monte Carlo simulation the phase structure of noncommutative $U(1)$ gauge theory in two dimensions using the fuzzy sphere as a non-perturbative regulator. There are three phases of the model. The boundary between the matrix phase which has no commutative analogue and the the fuzzy sphere phase is demarcated by the ${\bf S}^2_N-$to-matrix critical line. In the fuzzy sphere phase we observe the usual commutative weak-coupling and strong-coupling phases of gauge theory which are separated by the one-plaquette critical line. In other words the NC $U(1)$ model on the fuzzy sphere ${\bf S}^2_N$ in the fuzzy sphere phase acts like a commutative $U(N)$ gauge theory on a lattice (with two plaquettes). We also give the theoretical one-loop and $\frac{1}{N}$ expansion predictions for the ${\bf S}^2_N-$to-matrix and the one-plaquette critical lines respectively. It seems that near these lines these approximations are essentially exact. We also give a Monte Carlo measurement of the triple point where the three phases meet.

T. Quella
(King's College, London, UK)

Abstract:

Sigma models based on supergroups play a fundamental role in different areas of physics such as string theory, condensed matter theory and statistical physics. In this talk we will first outline some general differences to the case of ordinary groups. Afterwards a concrete application to strings in 3D AdS-space is discussed. Here we start with the solution of the WZW model for the supergroup PSU(1,1|2) which is based on a free fermion resolution and indicate how perturbations of this model give rise to string backgrounds with a mixture of Ramond-Ramond and Neveu-Schwarz fluxes.

A. Gerasimov
(ITEP, Moscow, Russia, and TCD and HMI, Dublin, Ireland)

Abstract:

An interpolation of special functions over various base fields will be discussed. The basic example is Whittaker function. The introduced interpolation technique is relevant to some problems in Arithmetic Geometry.

H. W. Braden
(Edinburgh University, UK)

Abstract:

Magnetic monopoles, or the topological soliton solutions of Yang-Mills-Higgs gauge theories in three space dimensions, have been objects of fascination for over a quarter of a century. BPS monopoles in particular have been the focus of much research. Many striking results are now known, yet, disappointingly, explicit solutions are rather few. We bring techniques from the study of finite dimensional integrable systems to bear upon the construction. The transcendental constraints of Hitchin may be replaced by (also transcendental) constraints on the period matrix. For a class of curves we show how these may be reduced to a number theoretic problem. A recently proven result of Ramanujan related to the hypergeometric function enables us to solve these and construct the corresponding monopoles.

J. L. Jaramillo
(Laboratoire Univers et Théories de l'Observatoire de Paris, Meudon, France)

Abstract:

We discuss the application of the recently introduced quasi-local formalisms for the study of black holes, to the numerical construction of spacetimes in a 3+1 approach. More specifically, we extract from this framework a set of boundary conditions, to be imposed on an inner sphere which represents a spatial slice of the black hole horizon. We illustrate the strategy by constructing initial data containing a black hole whose horizon is in quasi-equilibrium: we complete the elliptic system defined by the conformal thin sandwich equations with the here-discussed "isolated horizons" boundary conditions.

K. S. Gupta
(Saha Institute of Nuclear Physics, Calcutta, India)

D. Parashar
(Warwick University, UK)

P. Vitale
(Università Federico II and INFN, Naples, Italy)

T. Jonsson
(University of Iceland, Reykjavik, Iceland)

Abstract:

The geometry of random graphs and manifolds is reflected in the behaviour of random walks on these structures. We focus on the spectral dimension which is related to the return probability of a random walk to the starting point. We show how to calculate the spectral dimension for a large class of random combs as well as for generic random trees.

H. Römer
(Freiburg University, Germany)

D. Tong
(DAMTP, Cambridge, UK)

J.-P. Luminet
(Laboratoire Univers et Théories de l'Observatoire de Paris, Meudon, France)

Abstract:

What is the shape of the Universe? Is it curved or flat, finite or infinite? Is space "wraparound " to create ghost images of faraway cosmic sources? The lecture will introduce cosmic topology and review the most promising techniques using the cosmic microwave background radiation for detecting the topological properties of space within the next decade. It will discuss more particularly the proposal by Luminet et al. of a finite, positively curved, dodecahedral space as the best fit model for explaining the power spectrum of temperature anisotropies as observed by WMAP satellite.

S. Fredenhagen
(ETH, Zurich, Switzerland)

A. Konechny
(Rutgers University, Piscataway, USA)

E. Sharpe
(University of Utah, Salt Lake City, USA)

T. Wiseman
(Harvard University, Cambridge, USA)