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On factorizable S-matrices, generalized TTbar, and the Hagedorn transition

Journal of High Energy Physics volume 2021, Article number: 62 (2021) Cite this article

A preprint version of the article is available at arXiv.

Abstract

We study solutions of the Thermodynamic Bethe Ansatz equations for relativistic theories defined by the factorizable S-matrix of an integrable QFT deformed by CDD factors. Such S-matrices appear under generalized TTbar deformations of integrable QFT by special irrelevant operators. The TBA equations, of course, determine the ground state energy E(R) of the finite-size system, with the spatial coordinate compactified on a circle of circumference R. We limit attention to theories involving just one kind of stable particles, and consider deformations of the trivial (free fermion or boson) S-matrix by CDD factors with two elementary poles and regular high energy asymptotics — the “2CDD model”. We find that for all values of the parameters (positions of the CDD poles) the TBA equations exhibit two real solutions at R greater than a certain parameter-dependent value R*, which we refer to as the primary and secondary branches. The primary branch is identified with the standard iterative solution, while the secondary one is unstable against iterations and needs to be accessed through an alternative numerical method known as pseudo-arc-length continuation. The two branches merge at the “turning point” R* (a square-root branching point). The singularity signals a Hagedorn behavior of the density of high energy states of the deformed theories, a feature incompatible with the Wilsonian notion of a local QFT originating from a UV fixed point, but typical for string theories. This behavior of E(R) is qualitatively the same as the one for standard TTbar deformations of local QFT.

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Authors and Affiliations

  1. International Institute of Physics, Federal University of Rio Grande do Norte, Campus Universitário, Lagoa Nova, Natal, RN, 59078-970, Brazil

    Giancarlo Camilo & Thiago Fleury

  2. Quantum Research Centre, Technology Innovation Institute, Abu Dhabi, United Arab Emirates

    Giancarlo Camilo

  3. BME-MTA Statistical Field Theory ‘Lendület’ Research Group, Department of Theoretical Physics, Budapest University of Technology and Economics, Budafoki út 8, Budapest, 1111, Hungary

    Máté Lencsés

  4. Center for Cosmology and Particle Physics, New York University, New York, NY, 10003, USA

    Stefano Negro

  5. C.N. Yang Institute for Theoretical Physics, State University of New York, Stony Brook, NY, 11794-3840, USA

    Alexander Zamolodchikov

  6. Kharkevich Institute for Information Transmission Problems, Moscow, Russia

    Alexander Zamolodchikov

Authors
  1. Giancarlo Camilo
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  2. Thiago Fleury
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  3. Máté Lencsés
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  4. Stefano Negro
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  5. Alexander Zamolodchikov
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Correspondence to Thiago Fleury.

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Camilo, G., Fleury, T., Lencsés, M. et al. On factorizable S-matrices, generalized TTbar, and the Hagedorn transition. J. High Energ. Phys. 2021, 62 (2021). https://doi.org/10.1007/JHEP10(2021)062

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  • DOI: https://doi.org/10.1007/JHEP10(2021)062

Keywords

  • Integrable Field Theories
  • Renormalization Group