Decorating the gauge/YBE correspondence release_gyuha42gdfha7dzolgbopelj2q

by Erdal Catak, Mustafa Mullahasanoglu

Published in European Physical Journal C: Particles and Fields by Springer Science and Business Media LLC.

2024   Volume 84, Issue 9

Abstract

<jats:title>Abstract</jats:title> In this paper, we aim to study the three-dimensional <jats:inline-formula> <jats:alternatives> <jats:tex-math>$${\mathcal {N}}=2$$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> </jats:alternatives> </jats:inline-formula> supersymmetric dual gauge theories on <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$S_b^3/\mathbb {Z}_r$$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>S</mml:mi> <mml:mi>b</mml:mi> <mml:mn>3</mml:mn> </mml:msubsup> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>Z</mml:mi> <mml:mi>r</mml:mi> </mml:msub> </mml:mrow> </mml:math> </jats:alternatives> </jats:inline-formula> in the context of the gauge/YBE correspondence. We consider hyperbolic integral identities acquired via the equality of supersymmetric lens partition functions as solutions to the decoration transformation and the flipping relation in statistical mechanics. The solutions of those transformations aim at investigating various decorated lattice models possessing the Boltzmann weights of integrable Ising-like models obtained via the gauge/YBE correspondence. We also constructed The Bailey pairs for the decoration transformation and the flipping relation.
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