Comment on three-point function in AdS(3)/CFT(2)

TL;DR

This paper reviews the exact agreement of three-point functions in AdS3/CFT2, highlighting the mutual cancellation of worldsheet contributions and clarifying the relation between structure constants, thus supporting the AdS/CFT correspondence beyond supergravity.

Contribution

It provides a detailed analysis of the mutual cancellation mechanism in three-point functions and clarifies the relation between SU(2) and SL(2,R) structure constants in AdS3/CFT2.

Findings

Confirmed the mutual cancellation between AdS3 and S^3 contributions

Clarified the analytic relation between SU(2) and SL(2,R) structure constants

Discussed implications for four-point functions

Abstract

Recently, exact agreement has been found between bulk and boundary three-point functions in AdS_3 x S^3 x T^4 with NSNS fluxes. This represents a non-trivial check of AdS/CFT correspondence beyond the supergravity approximation as it corresponds to an exact worldsheet computation. When taking a closer look at this computation, one notices that a crucial point for the bulk-boundary agreement to hold is an intriguing mutual cancellation between worldsheet contributions corresponding to the AdS_3 and to the S^3 pieces of the geometry, what results in a simple factorized form for the final three-point function. In this note we review this cancellation and clarify some points about the analytic relation between the SU(2) and the SL(2,R) structure constants. In particular, we dicuss the connection to the Coulomb gas representation. We also make some comments on the four-point function.