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

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. 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 Bañados 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. 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.

arXiv comment30 pages, v2: references added, v3: minor clarifications, matches published version

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Cited by in corpus (8)

• $T\bar{T}$ in JT Gravity and BF Gauge Theory
• Field Theory of Interacting Boundary Gravitons
• Marginal $T\bar{T}$-Like Deformation and ModMax Theories in Two Dimensions
• Manifestly $SL(2,R)$ Duality-Symmetric Forms in ModMax Theory
• Entanglement Entropy and Modular Hamiltonian of free fermion with deformations on a torus
• Holographic Entanglement Entropy in $T\bar{T}$-deformed CFTs
• Systematic approach to correlators in $T\bar{T}$ deformed CFTs
• Root-$T\overline{T}$ deformed CFT partition functions at large central charge