Quantum chaos and the holographic principle

TL;DR

This paper reviews the development of low-dimensional holographic dualities involving quantum chaos, focusing on the SYK model and Jackiw-Teitelboim gravity, and discusses how string theory extends semiclassical gravity to resolve quantum scales.

Contribution

It provides an accessible review of chaos-assisted holography, connecting quantum chaos with gravity in two dimensions and exploring the role of string theory in resolving quantum gravitational scales.

Findings

Chaotic instabilities are key to holographic duality in low dimensions.

Quantum chaos signatures match between bulk and boundary theories.

String theory extensions are necessary for resolving quantum gravitational scales.

Abstract

Recent years have witnessed tremendous progress in developing a fine-grained low-dimensional holographic correspondence, specifically the construction of quantum mechanical boundary theories as holographic duals of two-dimensional gravity. In these developments, quantum chaos played a crucial role, both as source of universality and as a guiding principle for the matching of bulk and boundary signatures of gravity. In this article we review the construction of the chaos-assisted low-dimensional holographic correspondence for non-experts. We open with an introductory discussion of the two main protagonists of the theory, the SYK model and two-dimensional Jackiw-Teitelboim gravity. Within this framework we will discuss two independent 'bridges' between bulk and boundary physics, one pertaining to early time chaotic instabilities, the other to late time quantum chaos up to and including time scales of the order of the gravitational quantum level spacing. We will demonstrate that the resolution of these fine-grained quantum scales requires the extension of semiclassical gravity by elements of string theory. We conclude with an outlook towards higher dimensional generalizations of the chaotic holographic correspondence.