S-duality in $$ T\overline{T} $$-deformed CFT

$T\bar{T}$ deformed conformal field theories can be reformulated as worldsheet of non-critical strings. We use this correspondence to compute and study the partition sum a symmetric product CFT. find that it takes form second quantized string theory with given by seed CFT gaussian sigma model two-torus target space. show admits natural UV completion exhibits strong weak coupling $\mathbb{Z}_2$ duality interchanges momentum winding numbers maps $T\bar{T}$-coupling $\lambda$ its inverse $1/\lambda$. The is part full O$(2,2,\mathbb{Z})$-duality group includes PSL$(2,\mathbb{Z})$ acting on complexified coupling. symmetry eliminates appearance complex energies at for all CFTs central charge $c\leq 6$.