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

### Submission summary

 As Contributors: Monica Guica Arxiv Link: https://arxiv.org/abs/2012.15806v2 (pdf) Date accepted: 2021-03-02 Date submitted: 2021-01-14 07:08 Submitted by: Guica, Monica Submitted to: SciPost Physics Academic field: Physics Specialties: High-Energy Physics - Theory Approach: Theoretical

### 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.

Published as SciPost Phys. 10, 065 (2021)

### Submission & Refereeing History

Submission 2012.15806v2 on 14 January 2021

## Reports on this Submission

### Anonymous Report 2 on 2021-2-28 (Invited Report)

• Cite as: Anonymous, Report on arXiv:2012.15806v2, delivered 2021-02-28, doi: 10.21468/SciPost.Report.2631

see report

see report

### Report

This manuscript studies the apparent tension between the deformed energy level formula for a $J\bar{T}$ deformed CFT on the cylinder and the equally-spaced energies that follow from the symmetries. It is shown that the previously found infinite set of symmetry generators (which are field-dependent) does not act properly on the semiclassical phase space of the theory, but a new (infinite) set of symmetry generators does. These new generators preserve the algebra and have the correct charge and momentum quantization.

The manuscript is well-written, although sometimes a bit formal, and addresses a very important relevant issue in the $J\bar{T}$ literature. The proposed solution is valuable, not only for the $J\bar{T}$ deformation, but potentially also other deformations such as the $T\bar{T}$ deformation.

One confusion I had was with the rather formal expressions 3.40 and 3.49. Is it clear that these sums are convergent? Is the radius of convergence related to the complexification of the energy levels in 1.1?

Typo: It is Kac and not Ka\v{c}

Other than this minor confusion I recommend this manuscript for publication.

• validity: top
• significance: high
• originality: high
• clarity: high
• formatting: excellent
• grammar: excellent

### Anonymous Report 1 on 2021-2-11 (Invited Report)

• Cite as: Anonymous, Report on arXiv:2012.15806v2, delivered 2021-02-11, doi: 10.21468/SciPost.Report.2539

### Report

This work is a direct continuation of previous works of the author
on this topic, which deals with subtleties concerning symmetries
of solvable irrelevant deformed CFTs, and addresses new ideas
relevant for their resolution.

It is suitable for publication

• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -