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 $T\bar{T}$ 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 ($T\bar{T}$-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 ($T\bar{T}$-deformed) $\mathbb{R}\times \mathcal{N}$ seed of the boundary theory.

26 pages