On string theory on (deformed) \(Ad{S}_{3}\times {\mathbb{T}}^{3}\)

Abstract

We revisit the fermionic string theory on \(Ad{S}_{3}\times \mathcal{N}\) with k = 1, and its single-trace \(T\overline{T }\) deformation, with a focus on the (2, 2) superstring on (deformed) \(Ad{S}_{3}\times {\mathbb{T}}^{3}\). In a certain limit, it is dual to the symmetric product of the (\(T\overline{T }\)-deformed) SCFT₂ on \({\mathbb{R}}\times {\mathbb{T}}^{3}\). We present the winding-one delta-function normalizable worldsheet operators which, in the k = 1 decoupling limit, correspond to those of \({\mathbb{R}}\times {\mathbb{T}}^{3}\) in spacetime. We then demonstrate how their properties in string theory reproduce those of \({\mathbb{R}}\times {\mathbb{T}}^{3}\), or more generally, of a (\(T\overline{T }\)-deformed) \({\mathbb{R}}\times \mathcal{N}\) seed of the boundary theory.