Correlation functions of symmetric orbifold from AdS$_3$ string theory

TL;DR

This paper establishes a detailed correspondence between correlation functions in symmetric orbifold CFTs and string theory on AdS3, using the sl(2) WZNW model and Riemann surface techniques, advancing understanding of AdS3/CFT2 duality.

Contribution

It demonstrates how symmetric orbifold correlation functions can be reproduced from the sl(2) WZNW model via Riemann surface data and reduction to Liouville theory, extending to arbitrary genus surfaces.

Findings

Correlation functions of twist operators expressed via Riemann surface data.

Reproduction of these functions from the sl(2) WZNW model.

Generalization of the analysis to higher genus surfaces.

Abstract

The paper examines correspondence among correlation functions of symmetric orbifold and string theory on AdS3 described by sl(2) Wess-Zumino-Novikov-Witten (WZNW) model. We start by writing down n-point function of twist operators in the symmetric orbifold in terms of the data of effective Riemann surface. It is then shown that the correlation function can be reproduced from the sl(2) WZNW model. The computation is based on the claim that string worldsheet is given by the same Riemann surface and the reduction method from sl(2) WZNW model to Liouville field theory. We first consider the genus zero surface and then generalize the analysis to the case of generic genus. The result should be an important ingredient for deriving AdS$_3$/CFT$_2$ correspondence with tensionless superstrings to all orders in string perturbation theory.