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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.16230 |
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| _version_ | 1866910340092002304 |
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| author | Perez-Lona, A. Robbins, D. Sharpe, E. Vandermeulen, T. Yu, X. |
| author_facet | Perez-Lona, A. Robbins, D. Sharpe, E. Vandermeulen, T. Yu, X. |
| contents | In this paper we discuss gauging noninvertible zero-form symmetries in two dimensions. We specialize to certain gaugeable cases, specifically, fusion categories of the form Rep(H) for H a suitable Hopf algebra (which includes the special case Rep(G) for G a finite group). We also specialize to the case that the fusion category is multiplicity-free. We discuss how to construct a modular-invariant partition function from a choice of Frobenius algebra structure on H^*. We discuss how ordinary G orbifolds for finite groups G are a special case of the construction, corresponding to the fusion category Vec(G) = Rep( C[G]^* ). For the cases Rep(S_3), Rep(D_4), and Rep(Q_8), we construct the crossing kernels for general intertwiner maps. We explicitly compute partition functions in the examples of Rep(S_3), Rep(D_4), Rep(Q_8), and Rep(H_8), and discuss applications in c=1 CFTs. We also discuss decomposition in the special case that the entire noninvertible symmetry group acts trivially. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_16230 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Notes on gauging noninvertible symmetries, part 1: Multiplicity-free cases Perez-Lona, A. Robbins, D. Sharpe, E. Vandermeulen, T. Yu, X. High Energy Physics - Theory Strongly Correlated Electrons Quantum Algebra In this paper we discuss gauging noninvertible zero-form symmetries in two dimensions. We specialize to certain gaugeable cases, specifically, fusion categories of the form Rep(H) for H a suitable Hopf algebra (which includes the special case Rep(G) for G a finite group). We also specialize to the case that the fusion category is multiplicity-free. We discuss how to construct a modular-invariant partition function from a choice of Frobenius algebra structure on H^*. We discuss how ordinary G orbifolds for finite groups G are a special case of the construction, corresponding to the fusion category Vec(G) = Rep( C[G]^* ). For the cases Rep(S_3), Rep(D_4), and Rep(Q_8), we construct the crossing kernels for general intertwiner maps. We explicitly compute partition functions in the examples of Rep(S_3), Rep(D_4), Rep(Q_8), and Rep(H_8), and discuss applications in c=1 CFTs. We also discuss decomposition in the special case that the entire noninvertible symmetry group acts trivially. |
| title | Notes on gauging noninvertible symmetries, part 1: Multiplicity-free cases |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Quantum Algebra |
| url | https://arxiv.org/abs/2311.16230 |