Bogoliubov coefficients for the twist operator in the D1D5 CFT

TL;DR

This paper develops a technique using Bogoliubov coefficients to analyze the effect of the twist operator in the D1D5 CFT in the continuum limit, aiding understanding of black hole formation holographically.

Contribution

It introduces a new method to compute the twist operator's effect in the continuum limit, extending previous results and enabling analysis of higher-order interactions.

Findings

Reproduces known results for bosonic twist operators with winding numbers M and N.

Provides a framework for studying twist interactions at higher orders.

Offers insights into thermalization and black hole formation in holographic duals.

Abstract

The D1D5 CFT is a holographic dual of a near-extremal black hole in string theory. The interaction in this theory involves a twist operator which joins together different copies of a free CFT. Given a large number of D1 and D5 branes, the effective length of the circle on which the CFT lives is very large. We develop a technique to study the effect of the twist operator in the limit where the wavelengths of excitations are short compared to this effective length, which we call the 'continuum limit'. The method uses Bogoliubov coefficients to compute the effect of the twist operator in this limit. For bosonic fields, we use the method to reproduce recent results describing the effect of the twist operator when it links together CFT copies with windings M and N, producing a copy of winding M+N. We also comment on possible generalizations of our results. The methods developed here may help in understanding the twist interaction at higher orders. This in turn should provide insight into the thermalization process in the D1D5 CFT, which gives a holographic description of black hole formation.