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

Benjamin Doyon; Joseph Durnin; Takato Yoshimura

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

by Benjamin Doyon, Joseph Durnin, Takato Yoshimura

This is not the latest submitted version.

This Submission thread is now published as

SciPost Phys. 13, 072 (2022)

Submission summary

Authors (as registered SciPost users):

Takato Yoshimura

Submission information
Preprint Link:	https://arxiv.org/abs/2105.03326v4 (pdf)
Date submitted:	2021-12-30 17:08
Submitted by:	Yoshimura, Takato
Submitted to:	SciPost Physics

Ontological classification
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.

Author comments upon resubmission

We are grateful for the reviewer's constructive suggestion. It was indeed a little unclear what we meant by "derivation of TBA". The point here is that because we already argued in the previous sections that a generalised TTbar-deformed theory is an integrable system whose phase shift is

$\lambda_{\theta\phi}$ , the solution of the flow equations should naturally describe the thermodynamics of that integrable system. Now, what is shown in Appendix F is that the free energy as well as the free energy fluxes of an integrable system with the phase shift

$\lambda_{\theta\phi}$ , obtained from TBA, indeed satisfy the flow equations with an appropriate free theory intial condition (

$\lambda_{\theta\phi}=0$ ). Since these equations form a closed first-order system, the smooth solution must be unique. Hence this serves as a novel confirmation/derivation of TBA.

List of changes

1. We added the following sentence in Sect. 5: "To be more precise, we shall show that by solving the flowequations of a generalised $T\bar{T}$ -deformed theory parameterised by $\lambda_{\theta\phi}$ , which was shown to be equivalent to the integrable model whose phase shift is $\lambda_{\theta\phi}$ in Sect. 3, we obtain the free energy and the free energy fluxes that coincide with those of the corresponding integrable.

2. We replaced Appendic C with F in the last paragraph of Section 5.

Current status:

Has been resubmitted