Symmetry Topological Field Theory for Flavor Symmetry
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912332156764160 |
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| author | Jia, Qiang Luo, Ran Tian, Jiahua Wang, Yi-Nan Zhang, Yi |
| author_facet | Jia, Qiang Luo, Ran Tian, Jiahua Wang, Yi-Nan Zhang, Yi |
| contents | In this Letter, we demonstrate that the Symmetry Topological Field Theory (SymTFT) associated to a Quantum Field Theory (QFT) with continuous non-abelian $G$-flavor symmetry is a $BF$-theory with gauge group $G$. We show that gauging $G$-symmetry with a flat connection yields a theory with global symmetry characterized by exchanging the conjugate variables in the quantization of $BF$-theory. We construct the extended operators that generate the $G$-flavor symmetry and the $(d-2)$-form $\text{Rep}(G)$-symmetry of the gauged QFT. We demonstrate that $BF$-theory arises as the theory characterizing $G$-flavor symmetry of a QFT in the AdS/CFT setup. 't Hooft anomalies of the $G$-flavor symmetry are realized as extra terms in the action. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_04546 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symmetry Topological Field Theory for Flavor Symmetry Jia, Qiang Luo, Ran Tian, Jiahua Wang, Yi-Nan Zhang, Yi High Energy Physics - Theory In this Letter, we demonstrate that the Symmetry Topological Field Theory (SymTFT) associated to a Quantum Field Theory (QFT) with continuous non-abelian $G$-flavor symmetry is a $BF$-theory with gauge group $G$. We show that gauging $G$-symmetry with a flat connection yields a theory with global symmetry characterized by exchanging the conjugate variables in the quantization of $BF$-theory. We construct the extended operators that generate the $G$-flavor symmetry and the $(d-2)$-form $\text{Rep}(G)$-symmetry of the gauged QFT. We demonstrate that $BF$-theory arises as the theory characterizing $G$-flavor symmetry of a QFT in the AdS/CFT setup. 't Hooft anomalies of the $G$-flavor symmetry are realized as extra terms in the action. |
| title | Symmetry Topological Field Theory for Flavor Symmetry |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2503.04546 |