Infinite pseudo-conformal symmetries of classical T (T)over-bar, J (T)over-bar and J Ta - deformed CFTs

We show that T (T) over bar, J (T) over bar and J T-a - deformed classical CFTs posses 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 (T) over bar and J T-a deformations, we find two copies of a functional Witt - Kac-Moody algebra. In the case of the T (T) over bar deformation, we show that it is also possible to obtain two commuting copies of the Witt algebra.

Automated summary

This article demonstrates that T (T) over bar, J (T) over bar, and J T-a deformed classical CFTs have infinite symmetries, which are an extension of the infinitely-extended conformal and U (1) symmetries of the underlying two-dimensional CFT. Additionally, if the seed CFTs possess affine U (1) symmetry, it also survives in the deformed theories. The associated conserved charges form functional Witt-Kac-Moody algebra for J (T) over bar and J T-a deformations, while two commuting copies of the Witt algebra can be obtained for the T (T) over bar deformation.