Matrix Models for the Black Hole Information Paradox

TL;DR

This paper investigates matrix models as toy representations of gauge duals to AdS black holes, revealing how finite N effects restore information preservation by inducing spectral discreteness and correlator recurrences.

Contribution

It introduces and analyzes matrix models with charge-charge interactions, providing explicit 1/N^2 corrections and exploring the implications for the black hole information paradox.

Findings

At infinite N, models show continuous spectrum and information loss.

Finite N models have discrete spectrum and recurrences, indicating information preservation.

The order of limits (long-time vs. large-N) affects the interpretation of information loss.

Abstract

We study various matrix models with a charge-charge interaction as toy models of the gauge dual of the AdS black hole. These models show a continuous spectrum and power-law decay of correlators at late time and infinite N, implying information loss in this limit. At finite N, the spectrum is discrete and correlators have recurrences, so there is no information loss. We study these models by a variety of techniques, such as Feynman graph expansion, loop equations, and sum over Young tableaux, and we obtain explicitly the leading 1/N^2 corrections for the spectrum and correlators. These techniques are suggestive of possible dual bulk descriptions. At fixed order in 1/N^2 the spectrum remains continuous and no recurrence occurs, so information loss persists. However, the interchange of the long-time and large-N limits is subtle and requires further study.