Strings on NS-NS backgrounds as integrable deformations

Abstract

We consider the world-sheet S matrix of superstrings on an ${\mathrm{AdS}}_{3}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{3}\ifmmode\times\else\texttimes\fi{}{\mathrm{T}}^{4}$ NS-NS background in uniform light-cone gauge. We argue that scattering is given by a CDD factor that is nontrivial only between opposite-chirality particles, yielding a spin-chain-like Bethe ansatz. Our proposal reproduces the spectrum of nonprotected states computed from the Wess-Zumino-Witten description and the perturbative tree-level S matrix. This suggests that the model is an integrable deformation of a free theory similar to those arising from the $T\overline{T}$ composite operator.