Exact chiral ring of AdS3/CFT2

Abstract

We carry out an exact worldsheet computation of tree level threepoint correlators of chiral operators in type IIB string theory on AdS₃ × S³ × T⁴ with NS–NS flux. We present a simple representation for the string chiral operators in the coordinate basis of the dual boundary CFT. Striking cancelations occur between the three-point functions of the $\H_+^{3}$ and the SU(2) WZW models which result in a simple factorized form for the final correlators. We show, by fixing a single free parameter in the $\H_+^{3}$ WZW model, that the fusion rules and the structure constants of the N = 2 chiral ring in the bulk are in precise agreement with earlier computations in the boundary CFT of the symmetric product of T⁴ at the orbifold point in the large N limit.