English

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

High Energy Physics - Theory 2025-08-21 v3 Mathematical Physics math.MP Exactly Solvable and Integrable Systems

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.

Keywords

Cite

@article{arxiv.2306.13581,
  title  = {The star-square relation and the generalized star-triangle relation from 3d supersymmetric dualities I},
  author = {Mustafa Mullahasanoglu},
  journal= {arXiv preprint arXiv:2306.13581},
  year   = {2025}
}

Comments

minor corrections, accepted version