Correlators of the symmetric product orbifold

TL;DR

This paper introduces a symmetry-based method for computing correlation functions of twist fields in symmetric product orbifold conformal field theories, with implications for AdS3/CFT2 correspondence.

Contribution

It develops a novel approach using null vectors of the fractional Virasoro algebra to derive correlation functions purely from symmetry considerations.

Findings

New method for correlation functions in orbifold CFTs

Extension to subleading torus contributions

Implications for AdS3/CFT2 correspondence

Abstract

We exploit null vectors of the fractional Virasoro algebra of the symmetric product orbifold to compute correlation functions of twist fields in the large $N$ limit. This yields a new method to derive correlation functions in these orbifold CFTs that is purely based on the symmetry algebra. We explore various generalisations, such as subleading (torus) contributions or correlation functions of other fields than the bare twist fields. We comment on the consequences of our computation for the $\text{AdS}_3/\text{CFT}_2$ correspondence.