Full action of two deformation operators in the D1D5 CFT

TL;DR

This paper computes the full action of two deformation operators, including supercharges, in the D1D5 CFT to understand thermalization processes related to black hole formation.

Contribution

It extends previous work by calculating the supercharge action on twist operators, providing a complete description of two deformation operators' effects in the D1D5 CFT.

Findings

Full amplitude relates to twist-only amplitude via supercharge actions.

Contours are moved to initial and final states through conformal mappings.

The method enables analysis of thermalization in the D1D5 CFT.

Abstract

We are interested in thermalization in the D1D5 CFT, since this process is expected to be dual to black hole formation. We expect that the lowest order process where thermalization occurs will be at second order in the perturbation that moves us away from the orbifold point. The operator governing the deformation off of the orbifold point consists of a twist operator combined with a supercharge operator acting on this twist. In a previous paper we computed the action of two twist operators on an arbitrary state of the CFT. In the present work we compute the action of the supercharges on these twist operators, thereby obtaining the full action of two deformation operators on an arbitrary state of the CFT. We show that the full amplitude can be related to the amplitude with just the twists through an action of the supercharge operators on the initial and final states. The essential part of this computation consists of moving the contours from the twist operators to the initial and final states; to do this one must first map the amplitude to a covering space where the twists are removed, and then map back to the original space on which the CFT is defined.