Candidate Gaugings of Categorical Continuous Symmetry
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| Format: | Preprint |
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2026
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| _version_ | 1866908999073398784 |
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| author | Jia, Qiang Ma, Cheng Tian, Jiahua |
| author_facet | Jia, Qiang Ma, Cheng Tian, Jiahua |
| contents | Different gaugings of the global symmetry of a quantum field theory are closely related to its various phases. In this work, we study candidate gaugeable symmetries by analyzing candidate Lagrangian algebra data in the Drinfeld center of a symmetry category $\mathscr{C}^k(G)$ associated to a QFT with continuous global $G$-symmetry and possible 't Hooft anomaly labeled by an integer $k$. We use the combination of the $BF$ theory and the level-$k$ Chern-Simons theory with gauge group $G$ as a semiclassical kernel-theoretic model for the corresponding SymTFT. Under two explicit assumptions, namely that this $BF{+}k$CS theory provides the relevant SymTFT model and that the common $+1$ eigenspaces of the resulting modular kernels detect candidate Lagrangian algebra data in the continuous setting, we derive candidate modular $S$- and $T$-kernels from Hopf-link and framing correlators in $S^3$ semi-classically. We then use these kernels to obtain candidate modular invariants and candidate gaugings. The resulting formulas recover the established cases and suggest a possible extension of this kernel-theoretic picture to compact Lie groups. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_25820 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Candidate Gaugings of Categorical Continuous Symmetry Jia, Qiang Ma, Cheng Tian, Jiahua High Energy Physics - Theory Different gaugings of the global symmetry of a quantum field theory are closely related to its various phases. In this work, we study candidate gaugeable symmetries by analyzing candidate Lagrangian algebra data in the Drinfeld center of a symmetry category $\mathscr{C}^k(G)$ associated to a QFT with continuous global $G$-symmetry and possible 't Hooft anomaly labeled by an integer $k$. We use the combination of the $BF$ theory and the level-$k$ Chern-Simons theory with gauge group $G$ as a semiclassical kernel-theoretic model for the corresponding SymTFT. Under two explicit assumptions, namely that this $BF{+}k$CS theory provides the relevant SymTFT model and that the common $+1$ eigenspaces of the resulting modular kernels detect candidate Lagrangian algebra data in the continuous setting, we derive candidate modular $S$- and $T$-kernels from Hopf-link and framing correlators in $S^3$ semi-classically. We then use these kernels to obtain candidate modular invariants and candidate gaugings. The resulting formulas recover the established cases and suggest a possible extension of this kernel-theoretic picture to compact Lie groups. |
| title | Candidate Gaugings of Categorical Continuous Symmetry |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.25820 |