A Matrix Model for Black Hole Thermalization

TL;DR

This paper introduces a matrix model simulating black hole thermalization in gauge theories, highlighting how correlator decay differs at infinite versus finite N, with implications for the information paradox.

Contribution

It proposes a new toy matrix model capturing key features of black hole thermalization and analyzes correlator behavior using analytical and numerical methods.

Findings

Correlators decay to zero at infinite N

Finite N prevents correlator decay, modeling information retention

The model offers insights into the black hole information problem

Abstract

We present a matrix model which is intended as a toy model of the gauge dual of an AdS black hole. In particular, it captures the key property that at infinite $N$ correlators decay to zero on long time scales, while at finite $N$ this cannot happen. The model consists of a harmonic oscillator in the adjoint which acts as a heat bath for a particle in the fundamental representation. The Schwinger-Dyson equation reduces to a closed recursion relation, which we study by various analytical and numerical methods. We discuss some implications for the information problem.