https://doi.org/10.1140/epjp/s13360-024-05444-0
Regular Article
The star–square relation and the generalized star–triangle relation from 3d supersymmetric dualities I
Department of Physics, Bogazici University, Bebek, 34342, Istanbul, Turkey
a
mustafa.mullahasanoglu@std.bogazici.edu.tr
Received:
23
February
2024
Accepted:
11
July
2024
Published online:
21
July
2024
We study duality transformations of the star–square relation and the generalized star–triangle relation for Ising-like lattice spin models. The lattice spin 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.
© The Author(s) 2024
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