Abstract
The Toverline{T} deformed 2D CFTs correspond to AdS3 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 AdS3 gravity to construct the surface charges and associated algebra in Toverline{T} deformed theories. Starting from the Bañados geometry, we obtain the Chern-Simons gauge fields for the Toverline{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. The charge algebra turns out to be a non-linear deformed Virasoro algebra, which was obtained in different way by applying the cutoff perspective. Finally, we propose a way to construct the time-independent charges from these surface charges and they satisfy the field-dependent Virasoro algebra.
Highlights
Mixed boundary condition leads to a deformed bulk solution, which can be constructed by a field-dependent coordinate transformation [21]
The T Tdeformed 2D CFTs correspond to AdS3 gravity with Dirichlet boundary condition at finite cutoff or equivalently a mixed boundary condition at spatial infinity
It is proposed that the T Tdeformed 2D CFTs dual to the cutoff AdS3 with Dirichlet boundary condition or equivalently a mixed boundary condition
Summary
This section is to review some well-known facts about Chern-Simons theory following the refs. [63, 64]. We may get the different charges and symmetries by imposing various boundary conditions in Chern-Simons theory. The Poisson bracket of the smeared generator is a central extension of the algebra of the gauge generator (2.7). The asymptotic symmetry, called global symmetry, is defined as the quotient of the group of gauge transformations modulo the group of the trivial gauge transformations This is the origin of infinitely many boundary degrees of freedom in Chern-Simons theory. It turns out the surface charges satisfy the same Poisson bracket algebra. We would like to apply this approach to study the surface charges of the Chern-Simons gravity theory with the mixed boundary condition for T Tdeformation [21]
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