Global variants of $\mathcal{N}=1^*$ theories and Calogero-Moser systems
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918134638706688 |
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| author | Damia, Jeremías Aguilera Argurio, Riccardo Bourget, Antoine Tatitscheff, Valdo Vandepopeliere, Romain |
| author_facet | Damia, Jeremías Aguilera Argurio, Riccardo Bourget, Antoine Tatitscheff, Valdo Vandepopeliere, Romain |
| contents | Global variants of four-dimensional gauge theories are specified by their spectrum of genuine Wilson-'t Hooft line operators. The choice of global variant has significant consequences when spacetime is taken to be $\mathbb{R}^3 \times S^1$. We focus on $\mathcal N=1^*$ theories, which are closely connected to twisted elliptic Calogero-Moser systems. We establish, on general grounds, how this gauge-theoretic topological data manifests itself on the integrable system side by introducing a notion of global variants for complex many-body integrable systems associated with Lie algebras. Focusing on $\mathcal N=1^*$ theories of type $A$ and $B_2$, we elucidate the implications for the structure of gapped vacua, the emergent (generalized) symmetries realized in each vacuum, and the action of spontaneously broken modular invariance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01502 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global variants of $\mathcal{N}=1^*$ theories and Calogero-Moser systems Damia, Jeremías Aguilera Argurio, Riccardo Bourget, Antoine Tatitscheff, Valdo Vandepopeliere, Romain High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems Global variants of four-dimensional gauge theories are specified by their spectrum of genuine Wilson-'t Hooft line operators. The choice of global variant has significant consequences when spacetime is taken to be $\mathbb{R}^3 \times S^1$. We focus on $\mathcal N=1^*$ theories, which are closely connected to twisted elliptic Calogero-Moser systems. We establish, on general grounds, how this gauge-theoretic topological data manifests itself on the integrable system side by introducing a notion of global variants for complex many-body integrable systems associated with Lie algebras. Focusing on $\mathcal N=1^*$ theories of type $A$ and $B_2$, we elucidate the implications for the structure of gapped vacua, the emergent (generalized) symmetries realized in each vacuum, and the action of spontaneously broken modular invariance. |
| title | Global variants of $\mathcal{N}=1^*$ theories and Calogero-Moser systems |
| topic | High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2504.01502 |