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

TL;DR

This paper demonstrates that certain deformed classical 2D CFTs exhibit infinite, field-dependent conformal and U(1) symmetries, with algebraic structures resembling extended Witt and Kac-Moody algebras, revealing deep symmetry properties of these deformations.

Contribution

It uncovers infinite pseudo-conformal symmetries in $T ar T$, $J ar T$, and $J T_a$ deformed classical CFTs, extending the understanding of symmetries in these deformed theories.

Findings

Existence of infinite field-dependent conformal symmetries.

Survival of affine $U(1)$ symmetry in deformed theories.

Poisson brackets form two copies of Witt-Kac-Moody algebra.

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.