Abstract
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 \( \textrm{Rep}\left(\mathcal{H}\right) \) for \( \mathcal{H} \) 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 \( {\mathcal{H}}^{\ast } \). 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(S3), Rep(D4), and Rep(Q8), we construct the crossing kernels for general intertwiner maps. We explicitly compute partition functions in the examples of Rep(S3), Rep(D4), Rep(Q8), and \( \textrm{Rep}\left({\mathcal{H}}_8\right) \), and discuss applications in c = 1 CFTs. We also discuss decomposition in the special case that the entire noninvertible symmetry group acts trivially.
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Acknowledgments
We would like to thank N. Carqueville, C. M. Chang, Y. Choi, H. T. Lam, J. McNamara, T. Pantev, I. Runkel, S. H. Shao, Y. Tachikawa, Y. Wang, and Y. Zheng for useful discussions. We also thank the authors of [22] for communicating about their upcoming work and coordinating arXiv submission. E.S. was partially supported by NSF grant PHY-2310588. X.Y. was partially supported by NSF grant PHY-2014086.
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Perez-Lona, A., Robbins, D., Sharpe, E. et al. Notes on gauging noninvertible symmetries. Part I. Multiplicity-free cases. J. High Energ. Phys. 2024, 154 (2024). https://doi.org/10.1007/JHEP02(2024)154
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DOI: https://doi.org/10.1007/JHEP02(2024)154