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High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc
Abstract:
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. Starting from the Ba\~nados geometry, we obtained the
$T\bar{T}$ deformed Chern-Simons gauge fields which are parametrized by two
classes of independent charges. With help of the mixed boundary condition, the
residual gauge symmetries of deformed gauge fields and the associated surface
charges can be obtained respectively. These surface charges satisfy a
non-linear deformed Virasoro algebra, which is obtained differently in the
literature. Finally, the time-independent charges can be systematically
constructed from these surface charges and they satisfy the field-dependent
Virasoro algebra.
