# The Space of Integrable Systems from Generalised $T\bar{T}$-Deformations

### Submission summary

 As Contributors: Takato Yoshimura Arxiv Link: https://arxiv.org/abs/2105.03326v2 (pdf) Date submitted: 2021-06-25 17:17 Submitted by: Yoshimura, Takato Submitted to: SciPost Physics Academic field: Physics Specialties: High-Energy Physics - Theory Approach: Theoretical

### Abstract

We introduce an extension of the generalised $T\bar{T}$-deformation described by Smirnov-Zamolodchikov, to include the complete set of extensive charges. We show that this gives deformations of S-matrices beyond CDD factors, generating arbitrary functional dependence on momenta. We further derive from basic principles of statistical mechanics the flow equations for the free energy and all free energy fluxes. From this follows, without invoking the microscopic Bethe ansatz or other methods from integrability, that the thermodynamics of the deformed models are described by the integral equations of the thermodynamic Bethe-Ansatz, and that the exact average currents take the form expected from generalised hydrodynamics, both in the classical and quantum realms.

###### Current status:
Has been resubmitted

### Submission & Refereeing History

Resubmission 2105.03326v4 on 30 December 2021
Resubmission 2105.03326v3 on 17 September 2021

Submission 2105.03326v2 on 25 June 2021

## Reports on this Submission

### Report

The work of the authors meets the SciPost publication criteria. I do recommend publication on SciPost, following some minor amendments detailed in the Requested Changes section.

### Requested changes

1- In the second paragraph of Section 1, the authors cite some of the existing literature on TTbar deformations. The cite papers [8-14] following the phrase "The principles underlying TTbar-deformations have been extended to non-relativistic systems, where they are best expressed as charge-current deformations including higher-spin charges". Most of the cited works, however, deal with relativistic systems and all but two with the simple (non-generalized) TTbar deformation. Also, they cite the work [15], dealing with the standard TTbar and which appeared at the same time as [8], sparking the flurry of work on the subject, later, in a phrase referring to higher-spin TTbar models.
I suggest that the authors restructure this paragraph carefully, citing the existing literature with more attention. A work dealing with non-relativistic TTbar deformations they forgot to mention is, for example, "Conserved currents and TTbar_s​ irrelevant deformations of 2D integrable field theories" by Conti, Negro and Tateo, JHEP 11 (2019) 120; e-Print: 1904.09141.

2 - In the second paragraph of Section 2, the authors display the formula $\delta H \in T\Sigma^{\textrm{Int}}$, without mentioning what $T\Sigma^{\textrm{Int}}$ is. While this might be known to readers familiar with the work [8], I think it would be worth spending a few words on its meaning.

3 - Right after, in the phrase "Because the deformations form a Hamiltonian flow [...]", they probably meant "Because $\textbf{these}$ deformations form a Hamiltonian flow [...]".

4 - In the first paragraph on page 4, 5th line, they use the acronym SM, probably meaning Standard Model. I think it is always best to avoid acronyms that have not been previously explained, as widespread as their use can be.

5 - On page 5, 2nd line after eq (5), they refer to eq (42). This is probably due to a duplicate label in the TeX file since equations (5) and (42) are identical but in different places in the work. It is better to refer to (5) here.

6 - In the last paragraph of Section 6 the authors say "The generalisation of the deformation to this situation is presented in the appendix." It would be good to specify which of the appendices they refer to.

7 - In equations (34) to (36) the authors use the function $\chi$ having an inequality as argument. They should explain what this function is.

8 - In equation (76) the authors introduce a function $\rho$. They should explain what this function is.

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