On the Role of Chaos in the AdS/CFT Connection

TL;DR

This paper explores how chaos in non-linear systems like Yang-Mills theory can explain the thermalization process in the AdS/CFT correspondence, linking black hole formation to boundary theory dynamics.

Contribution

It proposes a mechanism where classical chaos induces self-thermalization in the boundary theory, connecting Lyapunov exponents to black hole absorption properties.

Findings

Chaotic dynamics in Yang-Mills theory can lead to boundary thermalization.

Imaginary part of gluon self-energy relates to black hole horizon absorption.

Self-thermalization explains black hole formation from pure states.

Abstract

The question of how infalling matter in a pure state forms a Schwarzschild black hole that appears to be at non-zero temperature is discussed in the context of the AdS/CFT connection. It is argued that the phenomenon of self-thermalization in non-linear (chaotic) systems can be invoked to explain how the boundary theory, initially at zero temperature self thermalizes and acquires a finite temperature. Yang-Mills theory is known to be chaotic (classically) and the imaginary part of the gluon self-energy (damping rate of the gluon plasma) is expected to give the Lyapunov exponent. We explain how the imaginary part would arise in the corresponding supergravity calculation due to absorption at the horizon of the black hole.