AdS_3/CFT_2 on torus in the sum over geometries

TL;DR

This paper explores the AdS$_3$/CFT$_2$ correspondence on a torus, demonstrating how correlation functions in the bulk relate to boundary CFT functions, especially in the sum over geometries and orbifold cases.

Contribution

It provides a detailed analysis of correlation functions in the AdS$_3$/CFT$_2$ setup on a torus, including the sum over geometries and orbifold cases, clarifying their factorization properties.

Findings

Correlation functions tend to standard CFT functions as regularization is removed.

Two-point functions factorize into conformal and anticonformal parts up to divergent volume terms.

Results hold for both regular and $Z_N$ orbifold geometries.

Abstract

We investigate the AdS$_3$/CFT$_2$ correspondence for the Euclidean AdS$_3$ space compactified on a solid torus with the CFT field on the regularizing boundary surface in the bulk. Correlation functions corresponding to the bulk theory at finite temperature tend to the standard CFT correlation functions in the limit of removed regularization. In both regular and $Z_N$ orbifold cases, in the sum over geometries, the two-point correlation function for massless modes factors, up to divergent terms proportional to the volume of the $SL(2,Z)/Z}$ group, into the finite sum of products of the conformal--anticonformal CFT Green's functions.