One-Loop Transition Amplitudes in the D1D5 CFT

TL;DR

This paper investigates how second-order twist deformations in the D1D5 CFT can lead to thermalization effects, providing explicit calculations of 1-loop transition amplitudes and their implications for black hole formation in the dual gravity theory.

Contribution

It introduces a detailed analysis of second-order twist deformations in the D1D5 CFT, deriving approximate expressions for transition amplitudes and establishing relationships for multi-twist processes.

Findings

Second-order twist deformations induce thermalization effects.

Explicit formulas for Bogoliubov coefficients in the continuum limit.

Relationships valid for arbitrary twist insertion processes.

Abstract

We consider the issue of thermalization in the D1D5 CFT. Thermalization is expected to correspond to the formation of a black hole in the dual gravity theory. We start from the orbifold point, where the theory is essentially free, and does not thermalize. In earlier work it was noted that there was no clear thermalization effect when the theory was deformed off the orbifold point to first order in the relevant twist perturbation. In this paper we consider the deformation to second order in the twist, where we do find effects that can cause thermalization of an initial perturbation. We consider a 1-loop process where two untwisted copies of the CFT are twisted to one copy and then again untwisted to two copies. We start with a single oscillator excitation on the initial CFT, and compute the effect of the two twists on this state. We find simple approximate expressions for the Bogoliubov coefficients and the behavior of the single oscillator excitation in the continuum limit, where the mode numbers involved are taken to be much larger than unity. We also prove a number of useful relationships valid for processes with an arbitrary number of twist insertions.