# A definition of primary operators in $J\bar T$-deformed CFTs

### Submission summary

 As Contributors: Monica Guica Arxiv Link: https://arxiv.org/abs/2112.14736v2 (pdf) Date accepted: 2022-05-31 Date submitted: 2022-02-14 06:18 Submitted by: Guica, Monica Submitted to: SciPost Physics Academic field: Physics Specialties: High-Energy Physics - Theory Approach: Theoretical

### Abstract

$J\bar T$-deformed CFTs provide an interesting example of non-local, yet UV-complete two-dimensional QFTs that are entirely solvable. They have been recently shown to possess an infinite set of symmetries, which are a continuous deformation of the Virasoro-Kac-Moody symmetries of the seed CFT. In this article, we put forth a definition of primary operators in $J\bar T$-deformed CFTs on a cylinder, which are singled out by having CFT-like momentum-space commutation relations with the symmetry generators in the decompatification limit. We show -- based on results we first derive for the case of $J^1 \wedge J^2$-deformed CFTs -- that all correlation functions of such operators in the $J\bar T$-deformed CFT can be computed exactly in terms of the correlation functions of the undeformed CFT and are crossing symmetric in the plane limit. In particular, two and three-point functions are simply given by the corresponding momentum-space correlator in the undeformed CFT, with all dimensions replaced by particular momentum-dependent conformal dimensions. Interestingly, scattering amplitudes off the near-horizon of extremal black holes are known to take a strikingly similar form.

###### Current status:
Publication decision taken: accept

Editorial decision: For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)

### Submission & Refereeing History

Submission 2112.14736v2 on 14 February 2022

## Reports on this Submission

### Strengths

1) The author proposes a definition for the notion of primary operators in the JJbar and JTbar deformed CFTs
2) The author computes some correlation functions of these operators and draws comparisons with the existing literature
3) The article is well structured, clear in its scope, and exhausting in its arguments and derivations

### Weaknesses

1) The reader can be easily confused by both the length of certain formulae and the notation which can be somewhat obscure in places

### Report

I believe this work satisfies the acceptance criteria of this journal and support its publication.

• validity: high
• significance: high
• originality: high
• clarity: good
• formatting: good
• grammar: good

### Strengths

1) New definition of operators in the $J{\bar T}$-deformed CFTs, which satisfy nice properties under the symmetry algebra
2) Computation of correlators of these operators on the plane
3) Clearly written with a detailed review of the well-understood $J{\bar J}$-deformation that motivates the construction

### Weaknesses

1) The definition of the operators does not follow from any first principles, though it satisfies many nice properties
2) The computations are done in a mixed formalism which starts from the cylinder but does the computations only in the infinite radius limit, it would be nicer to either compute precisely on the cylinder or to phrase everything directly on the plane

### Report

The paper suggests a definition of operators in $J{\bar T}$-deformed theories that transform nicely under the symmetry algebra of these theories (that was analyzed in detail in previous works by the author), and computes their correlation functions on the plane, with relatively simple results expressed as a shift in the conformal dimensions of the operators. The paper starts from an analysis of $J{\bar J}$-deformed theories, which are standard CFTs where the operators and correlators are well-understood, but which can also be analyzed in a language that can be generalized for $J{\bar T}$ deformations. The paper is clearly written and the results are nice and reasonable, in particular the advantages and disadvantages of the construction are described very clearly. I am happy to recommend the publication of this interesting paper in SciPost Physics.

### Requested changes

None

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