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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2404.16097 |
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| _version_ | 1866908898287419392 |
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| author | Zhang, Hao Y. |
| author_facet | Zhang, Hao Y. |
| contents | We propose that generalized symmetries in some string-constructed QFTs are given by K-theory. We thus have \textit{even-form} and \textit{odd-form} symmetries determined by $K_N(\partial X)$, the twisted K-theory as D-brane charges on the asymptotic boundary $\partial X$ of internal geometry $X$ with twist class $N$. For these QFTs, ``\textit{$p$-form symmetries}" are no longer separately well-defined for individual $p$, but are instead mixed together. We discuss 6D ADE-type (2,0) SCFTs and some 6d (1,0) LSTs as examples and demonstrate their twisted K-theoretic symmetries, and we checked them to be compatible with T-duality. We further point out, through explicit examples, that K-theory leads to symmetry extensions that cannot be detected by cohomology for Type II string theory on certain orbifolds of $\mathbb{C}^3$ and $\mathbb{C}^4$. We also discuss the implications of these results in the dual brane descriptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16097 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | K-theoretic Global Symmetry in String-constructed QFT and T-duality Zhang, Hao Y. High Energy Physics - Theory We propose that generalized symmetries in some string-constructed QFTs are given by K-theory. We thus have \textit{even-form} and \textit{odd-form} symmetries determined by $K_N(\partial X)$, the twisted K-theory as D-brane charges on the asymptotic boundary $\partial X$ of internal geometry $X$ with twist class $N$. For these QFTs, ``\textit{$p$-form symmetries}" are no longer separately well-defined for individual $p$, but are instead mixed together. We discuss 6D ADE-type (2,0) SCFTs and some 6d (1,0) LSTs as examples and demonstrate their twisted K-theoretic symmetries, and we checked them to be compatible with T-duality. We further point out, through explicit examples, that K-theory leads to symmetry extensions that cannot be detected by cohomology for Type II string theory on certain orbifolds of $\mathbb{C}^3$ and $\mathbb{C}^4$. We also discuss the implications of these results in the dual brane descriptions. |
| title | K-theoretic Global Symmetry in String-constructed QFT and T-duality |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2404.16097 |