Three-point functions in superstring theory on AdS3xS3xT4

TL;DR

The paper investigates spectral-flow sectors of type IIB string theory on $AdS_3\times S^3\times T^4$ and their holographic dual, focusing on three-point functions of spectral-flow images of chiral primaries. It constructs explicit vertex operators in NS and Ramond sectors, accounting for spectral flow, and computes spectral-flow conserving three-point functions on the sphere, including NS-NS-NS and RR-NS configurations. Through the bulk-to-boundary dictionary, the results are compared to correlators in the symmetric product orbifold CFT, with agreement found in the small string coupling limit, bolstering the AdS$_3$/CFT$_2$ correspondence for nontrivial spectral-flow sectors. The study reveals cancellations of certain constants across the SL(2,$\mathbb{R}$) and SU(2) factors and suggests avenues for extending the analysis to descendant states and deeper spectral-flow structures in the AdS$_3$ WZNW model.

Abstract

We consider R and NS spectral flow sectors of type IIB superstring theory on AdS(3)xS(3)xT(4) in the context of the AdS(3)/CFT(2) correspondence. We present a derivation of the vertex operators creating spectral flow images of chiral primary states previously proposed in the literature. We compute spectral flow conserving three-point functions involving these operators on the sphere. Using the bulk-to-boundary dictionary, we compare the results with the corresponding correlators in the dual conformal field theory, the symmetric product orbifold of T(4). In the limit of small string coupling, agreement is found in all the cases considered.