The star-square relation and the generalized star-triangle relation from 3d supersymmetric dualities I
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911111283998720 |
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| author | Mullahasanoglu, Mustafa |
| author_facet | Mullahasanoglu, Mustafa |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_13581 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The star-square relation and the generalized star-triangle relation from 3d supersymmetric dualities I Mullahasanoglu, Mustafa High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems 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. |
| title | The star-square relation and the generalized star-triangle relation from 3d supersymmetric dualities I |
| topic | High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2306.13581 |