(1) Shreya Vardhan: Estimating time in quantum chaotic systems and black holes

Abstract: A time-evolved state in a unitary chaotic quantum many-body system macroscopically resembles a thermal density matrix. However, while a thermal density matrix does not evolve with time, a pure state undergoing unitary evolution must continue to evolve with time unless it is an energy eigenstate. We sharpen this difference by considering an information-theoretic task where we attempt to estimate the time for which the state has been evolved by making measurements on the state. We quantify the effectiveness of the time estimate using a quantity from quantum metrology called the quantum Fisher information (QFI). This quantity shows an interesting interplay between expectations from thermalization and constraints from unitarity. In the context of evaporating black holes, these results imply that the ability to make local time estimates suddenly improves after the Page time. 

(2) Herman Verlinde: Double Scaled SYK Model and de Sitter Holography

(3) Philip Argyres: Light ray operators and lightlike conformal defects

We show that large N matrix models (where the matrices depend only on time) have an exact boson description in 1+1 dimensions where space is naturally a lattice of spacing ~ 1/N embedded in a geometry dictated by the potential of the matrix model. We then show that the result can be extended to the c=1 matrix model, in which N is taken to infinity with a second parameter taken to zero with the product  \mu held fixed. The exact boson description now has a short distance cutoff proportional to 1/\mu. This bosonic description explains the uv finiteness of entanglement entropy and correlation functions of the c=1 matrix model. We compare this finiteness with 2D string theory. Generalisation of these ideas to matrix models in zero dimensions and to the theory of giant gravitons is discussed at the end. The first part is based on: "Exact lattice bosonization of finite N matrix quantum mechanics and c = 1", Ajay Mohan and GM,  e-Print: 2406.07629 [hep-th]

TBA

TBA

Taub-NUT-AdS spaces are characterized by their nut parameter "n" which leads to a string-like singularity, or Misner String, in certain classes of solutions. To remove these singularities, one must identify time coordinates which in turn messes up the thermodynamics. We proposed a new pair of thermodynamics variables that leads to consistent thermodynamics, i.e., first law, Gibbs-Duhem and Smarr's relations are all satisfied. We apply this thermodynamics to Dyonic Taub-NUT-AdS solutions with spherical, flat and hyperbolic horizon geometries. We have considered canonical and mixed ensembles to study the phase structure of these solutions. This study showed some intriguing features, which were not reported before, among which the existence of two distinguished critical points with a continuous phase transition region in between. Furthermore, in flat and hyperbolic cases we have found a continuous phase transition that takes place only for low enough pressures and temperatures, in contrast with the Van der Waals behavior that characterizes charged AdS black holes!

50 years after the duality of large N gauge theories to string theories was suggested, we still do not have a constructive method to find the string dual of a given gauge theory. I will review work in progress (in collaboration with S. Kundu, T. Sheaffer and L. Yung) on two approaches to understanding this, in what should perhaps be the simplest case, namely two dimensional gauge theories. The first approach uses perturbation theory to obtain an effective stringy description of 2d QCD with very massive adjoint fermions. The second approach starts from finding a good worldsheet description for the string dual to the two dimensional pure Yang-Mills theory.

Abstract: We canonically quantise Jackiw-Teitleboim  gravity in de Sitter space, with particular attention to the problem of time.  Our results suggest an holographic interpretation  for global deSitter space, in this two dimensional setting.

Abstract: The thermodynamic interpretation of Schwarzschild black holes has a rich history spanning five decades. In 1973 Bardeen et al. derived the laws of black hole mechanics which suggested a correspondence between (i) temperature and black hole’s mass, specifically T=(8πM)^-1 and (ii) entropy and black hole area: S=A/4. In 1975 Hawking found that a Schwarzschild black hole radiates as if it were a blackbody with temperature T=(8πM)^-1. This meant that the temperature-mass relationship discovered earlier was more than a correspondence. In 1977 Gibbons and Hawking proposed the action of Euclidean Schwarzschild (which also has T=(8πM)^-1) as a means to understand black hole thermodynamics. They recovered S=A/4.  

In this talk we will test if Euclidean Schwarzschild behaves like a heat bath for quantum matter that propagates on it. For simplicity we will use matter with restricted excitations – Ising spins. We will discover that increasing M causes the spins to undergo a second order phase transition from disorder to order and that the phase transition occurs at sub-Planckian M. 

Abstract: In constructing lattice versions of physical theories, usually the spacetime symmetries are given up. This is because of the use of difference approximation of the derivative operator which does not satisfy Leibniz rule. The same is responsible for the fermion doubling problem and the associated loss of chirality. We introduce a non-local lattice derivative, hereafter to be called logarithmic discrete derivative (LDD), as it admits a logarithmic expansion in powers of the difference operator and a formal lattice integral (LI) which is inverse of LDD. The pair (LDD, LI) can be shown to satisfy the same differential and integral calculi of the continuum. We demonstrate how the pair can be used to construct lattice theories with Poincaré invariance. A striking property of the resulting model is a local correspondence which says that local equations of the continuum theory still hold true on the lattice, site-wise. Although such a construction looks very formal in position space, in momentum space the action takes a simple form which may allow for numerical simulations. We show that the same momentum space results can also be obtained by using summation, instead of LI, by using a technique involving finer lattices. Similar concept was earlier arrived at by G. Bergner while studying SLAC-type non-local derivatives. We explain how LDD is related to SLAC derivative and indicate how the new understanding of locality in position space could potentially allow for more effective use of non-local derivatives in lattice studies. Time permitting, we shall also discus a generalisation of the construction to a class of curved backgrounds and another form of the lattice derivative that achieves the same thing but takes the form of an inverse sine hyperbolic function. 

Zoom: https://uky.zoom.us/my/shapere