Correlation functions in the $${\text{TsT}}/T\overline{T }$$ correspondence

Abstract

Abstract We investigate the proposed holographic duality between the TsT transformation of IIB string theory on AdS3 × $$\mathcal{N}$$ with NS-NS flux and a single-trace $$T\overline{T }$$ deformation of the symmetric orbifold CFT. We present a non-perturbative calculation of two-point correlation functions using string theory and demonstrate their consistency with those of the $$T\overline{T }$$ deformation. The two-point correlation function of the deformed theory on the plane, written in momentum space, is obtained from that of the undeformed theory by replacing h with $$h+2\frac{\widetilde{\lambda }}{w}p\overline{p }$$, where h is the spacetime conformal weight, $$\widetilde{\lambda }$$ is a deformation parameter, p and $$\overline{p }$$ are the momenta, and w labels the twisted sectors in the deformed symmetric product. At w = 1, the non-perturbative result satisfies the Callan-Symanzik equation for double-trace $$T\overline{T }$$ deformed CFT derived in [1]. We also perform conformal perturbations on both the worldsheet CFT and the symmetric orbifold CFT as a sanity check. The perturbative and non-perturbative matching between results on the two sides provides further evidence of the conjectured $${\text{TsT}}/T\overline{T }$$ correspondence.