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\( T\overline{T} \)-deformation of q-Yang-Mills theory

  • Regular Article - Theoretical Physics
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  • Published: 17 November 2020
  • volume 2020, Article number: 86 (2020)
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\( T\overline{T} \)-deformation of q-Yang-Mills theory
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  • Leonardo Santilli1,
  • Richard J. Szabo2,3,4 &
  • Miguel Tierz5,1 

  • 243 Accesses

  • 10 Citations

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A preprint version of the article is available at arXiv.

Abstract

We derive the \( T\overline{T} \)-perturbed version of two-dimensional q-deformed Yang-Mills theory on an arbitrary Riemann surface by coupling the unperturbed theory in the first order formalism to Jackiw-Teitelboim gravity. We show that the \( T\overline{T} \)-deformation results in a breakdown of the connection with a Chern-Simons theory on a Seifert manifold, and of the large N factorization into chiral and anti-chiral sectors. For the U(N) gauge theory on the sphere, we show that the large N phase transition persists, and that it is of third order and induced by instantons. The effect of the \( T\overline{T} \)-deformation is to decrease the critical value of the ’t Hooft coupling, and also to extend the class of line bundles for which the phase transition occurs. The same results are shown to hold for (q, t)-deformed Yang-Mills theory. We also explicitly evaluate the entanglement entropy in the large N limit of Yang-Mills theory, showing that the \( T\overline{T} \)-deformation decreases the contribution of the Boltzmann entropy.

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Authors and Affiliations

  1. Grupo de Física Matemática, Departamento de Matemática, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Edifício C6, 1749-016, Lisboa, Portugal

    Leonardo Santilli & Miguel Tierz

  2. Department of Mathematics, Heriot-Watt University, Colin Maclaurin Building, Riccarton, Edinburgh, EH14 4AS, U.K.

    Richard J. Szabo

  3. Maxwell Institute for Mathematical Sciences, Bayes Centre, 47 Potterrow, Edinburgh, EH8 9BT, U.K.

    Richard J. Szabo

  4. Higgs Centre for Theoretical Physics, James Clerk Maxwell Building, Kings Buildings, Edinburgh, EH9 3JZ, U.K.

    Richard J. Szabo

  5. Departamento de Matemática, ISCTE — Instituto Universitário de Lisboa, Avenida das Forças Armadas, 1649-026, Lisboa, Portugal

    Miguel Tierz

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  1. Leonardo Santilli
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Correspondence to Miguel Tierz.

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Santilli, L., Szabo, R.J. & Tierz, M. \( T\overline{T} \)-deformation of q-Yang-Mills theory. J. High Energ. Phys. 2020, 86 (2020). https://doi.org/10.1007/JHEP11(2020)086

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  • Received: 13 September 2020

  • Accepted: 13 October 2020

  • Published: 17 November 2020

  • DOI: https://doi.org/10.1007/JHEP11(2020)086

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Keywords

  • Field Theories in Lower Dimensions
  • Nonperturbative Effects
  • Matrix Models
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