  Starting from holography for IIB string theory on AdS$_3\times \mathcal N$
with NS-NS flux, the TsT/$T\bar T$ correspondence is a conjecture that a TsT
transformation on the string theory side is holographically dual to the
single-trace version of the $T\bar T$ 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
$T\bar T$-deformed CFT$_2$. 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 $T\bar T$ deformed CFT$_2$.
