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2021

Surface charges in Chern-Simons gravity with $T\bar{T}$ deformation

He, Miao, He, Song, Gao, Yi-hong

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The $T\bar{T}$ deformed 2D CFTs correspond to AdS$_3$ gravity with Dirichlet boundary condition at finite cutoff or equivalently a mixed boundary condition at spatial infinity.

In this work, we use the latter perspective and Chern-Simons formalism of AdS$_3$ gravity to construct the surface charges and associated algebra in $T\bar{T}$ deformed theories.
Starting from the Ba\~nados geometry, we obtain the Chern-Simons gauge fields for the $T\bar{T}$ deformed geometry, which are parametrized by two independent charges.
With help of the mixed boundary condition, the residual gauge symmetries of the deformed gauge fields and the associated surface charges were obtained respectively.

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