Thermalization in the D1D5 CFT

TL;DR

The paper argues that black hole formation in gravity corresponds to a phase of thermalization in the dual CFT, which involves a transition to fuzzball states after large redshift effects, supported by computations of scattering processes in the D1D5 CFT.

Contribution

It introduces a new perspective on thermalization in the D1D5 CFT, distinguishing it from mere redshift effects and providing explicit calculations of scattering vertices leading to thermalization.

Findings

Large redshift does not imply thermalization in the CFT.

Thermalization involves a transition to fuzzball states.

Secular growth in amplitudes may signal thermalization processes.

Abstract

It is generally agreed that black hole formation in gravity corresponds to thermalization in the dual CFT. It is sometimes argued that if the CFT evolution shows evidence of large redshift in gravity, then we have seen black hole formation in the CFT. We argue that this is not the case: a clock falling towards the horizon increases its redshift but remains intact as a clock; thus it is not `thermalized'. Instead, thermalization should correspond to a new phase after the phase of large redshift, where the infalling object turns into fuzzballs on reaching within planck distance of the horizon. We compute simple examples of the scattering vertex in the D1D5 CFT which, after many iterations, would lead to thermalization. An initial state made of two left-moving and two right-moving excitations corresponds, in gravity, to two gravitons heading towards each other. The thermalization vertex in the CFT breaks these excitations into multiple excitations on the left and right sides; we compute the amplitudes for several of these processes. We find secular terms that grow as $t^2$ instead of oscillating with $t$; we conjecture that this may be a feature of processes leading to thermalization.