Infinite $\mathrm{T}\bar{\mathrm{T}}$-like symmetries of compactified LST

We show that the three-dimensional asymptotically linear dilaton background that arises in the near-horizon decoupling region of NS5-branes compactified on $T^4$ admits boundary conditions that lead to an infinite set of symmetries. The associated conserved charges, which implement field-dependent coordinate transformations, are found to be identical to the corresponding generators in a symmetric product orbifold of $T\bar{T}$ - deformed CFTs. Their algebra is a non-linear modification of the $\mathrm{V}\mathrm{i}\mathrm{r}\mathrm{a}\mathrm{s}\mathrm{o}\mathrm{r}\mathrm{o}\times \mathrm{V}\mathrm{i}\mathrm{r}\mathrm{a}\mathrm{s}\mathrm{o}\mathrm{r}\mathrm{o}$ algebra, which precisely coincides with the algebra of the “unrescaled” symmetry generators in $T\bar{T}$-deformed CFTs. This further strengthens a previously proposed link between the single-trace $T\bar{T}$ deformation and compactified little string theory.