$T\bar{T}/J\bar{T}$-deformed WZW models from Chern-Simons AdS$_3$ gravity with mixed boundary conditions

Understand

In this work we consider AdS$_3$ gravitational theory with certain mixed boundary conditions at spatial infinity.

• Using the Chern-Simons formalism of AdS$_3$ gravity, we find that these boundary conditions lead to non-trivial boundary terms, which, in turn, produce exactly the spectrum of the $T\bar{T}/J\bar{T}$-deformed CFTs.
• We then follow the procedure for constructing asymptotic boundary dynamics of AdS$_3$ to derive the constrained $T\bar{T}$-deformed WZW model from Chern-Simons gravity.
• The resulting theory turns out to be the $T\bar{T}$-deformed Alekseev-Shatashvili action after disentangling the constraints.