Symmetries versus the spectrum of $ J\bar T$-deformed CFTs

TL;DR

This paper resolves a discrepancy in $J\bar T$-deformed CFTs by introducing new conserved charges related to classical symmetries, aligning the algebra with the finite-size spectrum through an energy-dependent spectral flow.

Contribution

It introduces a new set of classical conserved charges that reconcile the symmetry algebra with the finite-size spectrum of $J\bar T$-deformed CFTs via spectral flow.

Findings

New conserved charges are consistent with semi-classical quantization.

The energy operator is outside the spectrally flowed sector.

The symmetry algebra and spectrum are now compatible.

Abstract

It has been recently shown that classical $J\bar T$ - deformed CFTs possess an infinite-dimensional Witt-Ka\v{c}-Moody symmetry, generated by certain field-dependent coordinate and gauge transformations. On a cylinder, however, the equal spacing of the descendants' energies predicted by such a symmetry algebra is inconsistent with the known finite-size spectrum of $J\bar T$ - deformed CFTs. Also, the associated quantum symmetry generators do not have a proper action on the Hilbert space. In this article, we resolve this tension by finding a new set of (classical) conserved charges, whose action is consistent with semi-classical quantization, and which are related to the previous symmetry generators by a type of energy-dependent spectral flow. The previous inconsistency between the algebra and the spectrum is resolved because the energy operator does not belong to the spectrally flowed sector.