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arXiv · 2306.13581

The star-square relation and the generalized star-triangle relation from 3d supersymmetric dualities I

Mustafa Mullahasanoglu
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Abstract

We study duality transformations of the star-square relation and the generalized star-triangle relation for Ising-like integrable lattice spin models. The integrable models are obtained via gauge/YBE correspondence which connects the supersymmetric gauge theories and lattice spin models of statistical mechanics. By the use of integral identities coming from the duality of three-dimensional supersymmetric gauge theories, we construct hyperbolic, lens hyperbolic, trigonometric, and rational solutions to the duality transformations. These duality transformations allow us to construct spin lattice models with four-spin (the star-square relation) and three-spin (the generalized star-triangle relation) interactions.

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Mustafa Mullahasanoglu. 2023-06-23. The star-square relation and the generalized star-triangle relation from 3d supersymmetric dualities I. https://arxiv.org/abs/2306.13581

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