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

by Monica Guica, Ruben Monten

Submission summary

As Contributors: Ruben Monten
Arxiv Link: https://arxiv.org/abs/2011.05445v2 (pdf)
Date accepted: 2021-09-15
Date submitted: 2021-08-16 19:23
Submitted by: Monten, Ruben
Submitted to: SciPost Physics
Academic field: Physics
Specialties:
  • High-Energy Physics - Theory
Approach: Theoretical

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.

Published as SciPost Phys. 11, 078 (2021)



Author comments upon resubmission

  • Updated the discussion concerning the additional constraints on the undetermined functions in the TTbar-deformed charge algebra.
  • Corrected typos.

Reports on this Submission

Anonymous Report 1 on 2021-9-11 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2011.05445v2, delivered 2021-09-11, doi: 10.21468/SciPost.Report.3520

Report

I am happy to accept this article for publication. My question based on confusion has been clarified by the authors. I apologize to the authors for taking an unnecessarily long time to review the revision.

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