Correlation functions in the D1-D5 orbifold CFT

TL;DR

This paper derives universal explicit formulas for correlation functions involving twist operators in the D1-D5 orbifold CFT, aiding the understanding of black hole microstates and their holographic duals.

Contribution

It provides the first explicit, universal expressions for correlation functions involving twist operators in the D1-D5 orbifold CFT, independent of the target space.

Findings

Derived explicit formulas for twist operator correlation functions

Formulas are universal, independent of target space choice

Results facilitate matching of microstates with supergravity solutions

Abstract

The D1-D5 system has an orbifold point in its moduli space, at which it may be described by an ${\cal N} = (4,4)$ supersymmetric sigma model with target space $M^N/S(N)$ where $M$ is $\mathbb{T}^4$ or $K3$. In this paper we consider correlation functions involving chiral operators constructed from twist fields: we find explicit expressions for processes involving a twist $n$ operator joining $n$ twist operators of arbitrary twist. These expressions are universal, in that they are independent of the choice of $M$, and the final results can be expressed in a compact form. We explain how these results are relevant to the black hole microstate programme: one point functions of chiral operators can be used to reconstruct AdS$_3$ near horizon regions of D1-D5 microstates and to match microstates constructed in supergravity with the CFT.