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

A bstract 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) SCFT 2 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.