Thermodynamic Bethe Ansatz past turning points: the (elliptic) sinh-Gordon model

Lucía Córdova (Institut de Physique Théorique Philippe Meyer, Laboratoire de Physique de l’École Normale Supérieure, PSL University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, 24 rue Lhomond, Paris Cedex 05, 75231, France) ; Stefano Negro (Center for Cosmology and Particle Physics, New York University, New York, NY, 10003, USA) ; Fidel Schaposnik Massolo (Institut des Hautes Études Scientifiques, 35 route de Chartres, Bures-sur-Yvette, 91440, France)

We analyze the Thermodynamic Bethe Ansatz (TBA) for various integrable S-matrices in the context of generalized T T ¯ $$ \overline{\mathrm{T}} $$ deformations. We focus on the sinh-Gordon model and its elliptic deformation in both its fermionic and bosonic realizations. We confirm that the determining factor for a turning point in the TBA, interpreted as a finite Hagedorn temperature, is the difference between the number of bound states and resonances in the theory. Implementing the numerical pseudo-arclength continuation method, we are able to follow the solutions to the TBA equations past the turning point all the way to the ultraviolet regime. We find that for any number k of resonances the pair of complex conjugate solutions below the turning point is such that the effective central charge is minimized. As k → ∞ the UV effective central charge goes to zero as in the elliptic sinh-Gordon model. Finally we uncover a new family of UV complete integrable theories defined by the bosonic counterparts of the S-matrices describing the Φ1,3 integrable deformation of non-unitary minimal models M $$ \mathcal{M} $$ 2,2n+3.

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      "surname": "C\u00f3rdova", 
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      "surname": "Negro", 
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  "abstracts": [
    {
      "source": "Springer", 
      "value": "We analyze the Thermodynamic Bethe Ansatz (TBA) for various integrable S-matrices in the context of generalized T  <math> <mover> <mi>T</mi> <mo>\u00af</mo> </mover> </math>  $$ \\overline{\\mathrm{T}} $$  deformations. We focus on the sinh-Gordon model and its elliptic deformation in both its fermionic and bosonic realizations. We confirm that the determining factor for a turning point in the TBA, interpreted as a finite Hagedorn temperature, is the difference between the number of bound states and resonances in the theory. Implementing the numerical pseudo-arclength continuation method, we are able to follow the solutions to the TBA equations past the turning point all the way to the ultraviolet regime. We find that for any number k of resonances the pair of complex conjugate solutions below the turning point is such that the effective central charge is minimized. As k \u2192 \u221e the UV effective central charge goes to zero as in the elliptic sinh-Gordon model. Finally we uncover a new family of UV complete integrable theories defined by the bosonic counterparts of the S-matrices describing the \u03a61,3 integrable deformation of non-unitary minimal models   <math> <mi>M</mi> </math>  $$ \\mathcal{M} $$  2,2n+3."
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Published on:
10 January 2022
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2022 (2022)
Issue 1
Pages 1-34
DOI:
https://doi.org/10.1007/JHEP01(2022)035
arXiv:
2110.14666
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: