(-1)-form symmetries from M-theory and SymTFTs
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| Format: | Preprint |
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2024
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| _version_ | 1866912223025168384 |
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| author | Najjar, Marwan Santilli, Leonardo Wang, Yi-Nan |
| author_facet | Najjar, Marwan Santilli, Leonardo Wang, Yi-Nan |
| contents | We explore $(-1)$-form symmetries within the framework of geometric engineering in M-theory. By constructing the Symmetry Topological Field Theory (SymTFT) for selected 5d $\mathcal{N}=1$, 4d $\mathcal{N}=2$ and 4d $\mathcal{N}=1$ theories, we formalize the geometric origin of these symmetries and compute the mixed anomaly polynomials involving $(-1)$-form and higher-form symmetries. Our findings consistently reveal both discrete and continuous $(-1)$-form symmetries, aligning with established field theory results, while also uncovering new $(-1)$-form symmetry factors and structural insights. In particular, we study the SymTFT of 4d $\mathcal{N}=1$ theories from M-theory on a class of spaces with $G_2$ holonomy, and obtain properties such as modified instanton sums and 4-group structures observed in other 4d gauge theories. Additionally, we systematically construct symmetry operators for continuous abelian symmetries, refining existing proposals, and providing an M-theory origin for them. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_19683 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | (-1)-form symmetries from M-theory and SymTFTs Najjar, Marwan Santilli, Leonardo Wang, Yi-Nan High Energy Physics - Theory We explore $(-1)$-form symmetries within the framework of geometric engineering in M-theory. By constructing the Symmetry Topological Field Theory (SymTFT) for selected 5d $\mathcal{N}=1$, 4d $\mathcal{N}=2$ and 4d $\mathcal{N}=1$ theories, we formalize the geometric origin of these symmetries and compute the mixed anomaly polynomials involving $(-1)$-form and higher-form symmetries. Our findings consistently reveal both discrete and continuous $(-1)$-form symmetries, aligning with established field theory results, while also uncovering new $(-1)$-form symmetry factors and structural insights. In particular, we study the SymTFT of 4d $\mathcal{N}=1$ theories from M-theory on a class of spaces with $G_2$ holonomy, and obtain properties such as modified instanton sums and 4-group structures observed in other 4d gauge theories. Additionally, we systematically construct symmetry operators for continuous abelian symmetries, refining existing proposals, and providing an M-theory origin for them. |
| title | (-1)-form symmetries from M-theory and SymTFTs |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2411.19683 |