Asymptotic symmetries in the $TsT/T\bar{T}$ correspondence

Starting from holography for IIB string theory on AdS_3× \mathcal N3×𝒩 with NS-NS flux, the TsT/T\bar TTT‾ correspondence is a conjecture that a TsT transformation on the string theory side is holographically dual to the single-trace version of the T\bar TTT‾ deformation on the field theory side. More precisely, the long string sector of string theory on the TsT-transformed background corresponds to the symmetric product theory whose seed theory is the T\bar TTT‾-deformed CFT_22. In this paper, we study the asymptotic symmetry of the string theory in the bulk. We find a state-dependent, non-local field redefinition under which the worldsheet equations of motion, stress tensor, as well as the symplectic form of string theory after the TsT transformation are mapped to those before the TsT transformation. The asymptotic symmetry in the auxiliary AdS basis is generated by two commuting Virasoro generators, while in the TsT transformed basis is non-linear and non-local. Our result from string theory analysis is compatible with that of the T\bar TTT‾ deformed CFT_22.