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A general definition of $JT_a$  deformed QFTs
by Tarek Anous, Monica Guica
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Submission summary
Authors (as registered SciPost users):  Tarek Anous 
Submission information  

Preprint Link:  https://arxiv.org/abs/1911.02031v2 (pdf) 
Date accepted:  20210419 
Date submitted:  20210128 09:49 
Submitted by:  Anous, Tarek 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Abstract
We propose a general pathintegral definition of twodimensional quantum field theories deformed by an integrable, irrelevant vector operator constructed from the components of the stress tensor and those of a $U(1)$ current. The deformed theory is obtained by coupling the original QFT to a flat dynamical gauge field and "half" a flat dynamical vielbein. The resulting partition function is shown to satisfy a geometric flow equation, which perfectly reproduces the flow equations for the deformed energy levels that were previously derived in the literature. The Smatrix of the deformed QFT differs from the original Smatrix only by an overall phase factor that depends on the charges and momenta of the external particles, thus supporting the conjecture that such QFTs are UV complete, although intrinsically nonlocal. For the special case of an integrable QFT, we check that this phase factor precisely reproduces the change in the finitesize spectrum via the Thermodynamic Bethe Ansatz equations.
Published as SciPost Phys. 10, 096 (2021)
Submission & Refereeing History
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Reports on this Submission
Anonymous Report 2 on 202148 (Invited Report)
 Cite as: Anonymous, Report on arXiv:1911.02031v2, delivered 20210408, doi: 10.21468/SciPost.Report.2766
Report
The authors approach the analysis of the JT deformation from the path integral point of view. In this framework they derive the partition function as a path integral transform and use this result to derive an equation for the spectrum. Then they solve this equation finding results matching the literature. Moreover they derive the dressing factor for the Smatrix, again, agreeing with past analyses.
The paper is clear and well written and I suggest it for publication on SciPost.
Anonymous Report 1 on 202148 (Invited Report)
 Cite as: Anonymous, Report on arXiv:1911.02031v2, delivered 20210408, doi: 10.21468/SciPost.Report.2765
Report
This paper gives a nice account of a variety of approaches to the JT deformation, in analogy to he various methods that have been used to study TTbar. In particular a thorough account is given of a path integral definition of the deformation. The paper is well written and also serves as a useful survey of the state of the art for the TTbar deformation. From the point of view of uniqueness, it would have been useful, but not necessary, to have had some discussion about boundary conditions on the pde (3.13) and to what extent they make its solution unique. (This is a problem for TTbar because the rhs is not elliptic). Also whether the spectral decomposition, which satisfies the pde termbyterm, in fact converges uniformly.