Thermalization in the D1D5 CFT

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.

The Dual of a Tidal Force in the D1D5 CFT

“…This is the same form we find in [40,41,42]. We find the following limits for the sums k min (m, n, p, q, r) = −2(m + n) k max (m, n, p, q, r) = 2(m + n) kmin (m, n, p, q, r) = −2m kmax (m, n, p, q, r) = 2m (4.10)…”

“…1. In this case, we show that though the splitting is 1 → 3 we still find a quadratic growth in the amplitude in time t. The same behavior which marked the 2 → 4 process computed in the vacuum state [40]. The final state containing three modes resembles a single particle stringy state in the superstratum geometry.…”

“…The oscillatory term in the amplitude, A 0→f ,osc m,n (t), can be interpreted [40,42] as the graviton propagating within the geometry starting from the boundary. If the geometry was just AdS 3 × S 3 × T 4 as is the case of NS vacuum studied in [40,42], the graviton would simply propagate from one side of the geometry to the other unhindered and then back again.…”

“…The CFT dual of a free falling graviton in AdS was studied in the context of the D1D5 CFT [40,41,42]. This involves applying two marginal deformations to a left and a right moving mode in the initial state which corresponds to a single graviton propagating in the gravity dual.…”

“…In [40,41] we also computed a 2 → 4 process: two left and two right moving modes splitting into four left and four right moving modes in the final state. The amplitude grows like t 2 instead of being periodic as in the 1 → 3 process.…”