Infinite pseudo-conformal symmetries of classical $T\bar{T}$, $J\bar{T}$ and $J{T}_a$ - deformed CFTs

Abstract

We show that $T\bar{T},J\bar{T}$ and $J{T}_a$ - deformed classical CFTs possess an infinite set of symmetries that take the form of a field-dependent generalization of two-dimensional conformal transformations. If, in addition, the seed CFTs possess an affine $U(1)$ symmetry, we show that it also survives in the deformed theories, again in a field-dependent form. These symmetries can be understood as the infinitely-extended conformal and $U(1)$ symmetries of the underlying two-dimensional CFT, seen through the prism of the "dynamical coordinates" that characterise each of these deformations. We also compute the Poisson bracket algebra of the associated conserved charges, using the Hamiltonian formalism. In the case of the $J\bar{T}$ and $J{T}_a$ deformations, we find two copies of a functional Witt - Kac-Moody algebra. In the case of the $T\bar{T}$ deformation, we show that it is also possible to obtain two commuting copies of the Witt algebra.

28 + 12 pages, added some corrections and clarifications

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• Infinite $\mathrm{T}\bar{\mathrm{T}}$-like symmetries of compactified LST
• Holographic entanglement entropy in $T\overline{T}$-deformed AdS${}_3$
• $T\overline{T}$-Like Flows and $3d$ Nonlinear Supersymmetry
• A definition of primary operators in $J\bar{T}$-deformed CFTs
• Flows in the Space of Interacting Chiral Boson Theories
• Surface charges in Chern-Simons gravity with $T\bar{T}$ deformation
• States, symmetries and correlators of $T\bar{T}$ and $J\bar{T}$ symmetric orbifolds
• Entanglement Entropy and Modular Hamiltonian of free fermion with deformations on a torus
• Irrelevant and marginal deformed BMS field theories
• Holographic Entanglement Entropy in $T\bar{T}$-deformed CFTs
• Systematic approach to correlators in $T\bar{T}$ deformed CFTs
• Locality and Conserved Charges in $T\overline{T}$-Deformed CFTs
• Field-Dependent Metrics and Higher-Form Symmetries in Duality-Invariant Theories of Non-Linear Electrodynamics
• Complete Minimal Form Factors for Irrelevant Deformations of Integrable Quantum Field Theory
• The on-shell action of supergravity & the B-side of TsT and single-trace $T\bar{T}$