### String Seminar

## Factorization of the Hilbert space of eternal black holes in general relativity

We generalize recent results in two-dimensional Jackiw-Teitelboim gravity to study factorization of the Hilbert space of eternal black holes in quantum gravity with a negative cosmological constant in any dimension. We approach the problem by computing the trace of two-sided observables as a sum over a recently constructed family of semiclassically well-controlled black hole microstates. These microstates, which contain heavy matter shells behind the horizon and form an overcomplete basis of the Hilbert space, exist in any theory of gravity with general relativity as its low energy limit. Using this representation of the microstates, we show that the trace of operators dual to functions of the Hamiltonians of the left and right holographic CFTs factorizes into a product over left and right factors to leading order in the semiclassical limit. Under certain conditions this implies factorization of the Hilbert space.

## Entanglement dynamics from universal low-lying modes

## Estimating time in quantum chaotic systems and black holes

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.

## The granularity of emergent geometry from Matrix models

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]

## Instantons, renormalons, and the failure of perturbation theory

TBA

## Dyonic Taub-NUT Phase Structures

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!