Notes on AdS_3

TL;DR

This paper investigates properties of AdS_3 conformal field theories using dualities with Sine-Liouville models, providing evidence for the duality and exploring supersymmetric extensions, with implications for D-branes in AdS_3.

Contribution

It offers new calculations of correlation functions in AdS_3 CFTs via duality, supporting the conjectured strong-weak coupling correspondence and extending to supersymmetric cases.

Findings

Agreement between different computational approaches supports the duality.

Different sectors of the spacetime CFT have varying Virasoro central charges.

Results facilitate future studies of D-branes in AdS_3.

Abstract

We use the conjectured strong-weak coupling worldsheet duality between the SL(2)/U(1) and Sine-Liouville conformal field theories to study some properties of degenerate operators and to compute correlation functions in CFT on AdS_3. The same quantities have been computed in the past by other means. The agreement between the different approaches provides new evidence for the duality. We also discuss the supersymmetric analog of this duality, the correspondence between SCFT on the cigar and N=2 Liouville. We show that in the spacetime CFT dual to string theory on AdS_3 via the AdS/CFT correspondence, the central term in the Virasoro algebra takes different values in different sectors of the theory. In a companion paper we use the results described here to study D-branes in AdS_3.