SymSETs and self-dualities under gauging non-invertible symmetries
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915102107631616 |
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| author | Lu, Da-Chuan Sun, Zhengdi Zhang, Zipei |
| author_facet | Lu, Da-Chuan Sun, Zhengdi Zhang, Zipei |
| contents | The self-duality defects under discrete gauging in a categorical symmetry $\mathcal{C}$ can be classified by inequivalent ways of enriching the bulk SymTFT of $\mathcal{C}$ with $\mathbb{Z}_2$ 0-form symmetry. The resulting Symmetry Enriched Topological (SET) orders will be referred to as $\textit{SymSETs}$ and are parameterized by choices of $\mathbb{Z}_2$ symmetries, as well as symmetry fractionalization classes and discrete torsions. In this work, we consider self-dualities under gauging $\textit{non-invertible}$ $0$-form symmetries in $2$-dim QFTs and explore their SymSETs. Unlike the simpler case of self-dualities under gauging finite Abelian groups, the SymSETs here generally admit multiple choices of fractionalization classes. We provide a direct construction of the SymSET from a given duality defect using its $\textit{relative center}$. Using the SymSET, we show explicitly that changing fractionalization classes can change fusion rules of the duality defect besides its $F$-symbols. We consider three concrete examples: the maximal gauging of $\operatorname{Rep} H_8$, the non-maximal gauging of the duality defect $\mathcal{N}$ in $\operatorname{Rep} H_8$ and $\operatorname{Rep} D_8$ respectively. The latter two cases each result in 6 fusion categories with two types of fusion rules related by changing fractionalization class. In particular, two self-dualities of $\operatorname{Rep} D_8$ related by changing the fractionalization class lead to $\operatorname{Rep} D_{16}$ and $\operatorname{Rep} SD_{16}$ respectively. Finally, we study the physical implications such as the spin selection rules and the SPT phases for the aforementioned categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07787 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | SymSETs and self-dualities under gauging non-invertible symmetries Lu, Da-Chuan Sun, Zhengdi Zhang, Zipei High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics The self-duality defects under discrete gauging in a categorical symmetry $\mathcal{C}$ can be classified by inequivalent ways of enriching the bulk SymTFT of $\mathcal{C}$ with $\mathbb{Z}_2$ 0-form symmetry. The resulting Symmetry Enriched Topological (SET) orders will be referred to as $\textit{SymSETs}$ and are parameterized by choices of $\mathbb{Z}_2$ symmetries, as well as symmetry fractionalization classes and discrete torsions. In this work, we consider self-dualities under gauging $\textit{non-invertible}$ $0$-form symmetries in $2$-dim QFTs and explore their SymSETs. Unlike the simpler case of self-dualities under gauging finite Abelian groups, the SymSETs here generally admit multiple choices of fractionalization classes. We provide a direct construction of the SymSET from a given duality defect using its $\textit{relative center}$. Using the SymSET, we show explicitly that changing fractionalization classes can change fusion rules of the duality defect besides its $F$-symbols. We consider three concrete examples: the maximal gauging of $\operatorname{Rep} H_8$, the non-maximal gauging of the duality defect $\mathcal{N}$ in $\operatorname{Rep} H_8$ and $\operatorname{Rep} D_8$ respectively. The latter two cases each result in 6 fusion categories with two types of fusion rules related by changing fractionalization class. In particular, two self-dualities of $\operatorname{Rep} D_8$ related by changing the fractionalization class lead to $\operatorname{Rep} D_{16}$ and $\operatorname{Rep} SD_{16}$ respectively. Finally, we study the physical implications such as the spin selection rules and the SPT phases for the aforementioned categories. |
| title | SymSETs and self-dualities under gauging non-invertible symmetries |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics |
| url | https://arxiv.org/abs/2501.07787 |