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Title: Notes on gauging noninvertible symmetries. Part I. Multiplicity-free cases
A<sc>bstract</sc> 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$$ \textrm{Rep}\left(\mathcal{H}\right) $$ Rep H for$$ \mathcal{H} $$ H a suitable Hopf algebra (which includes the special case Rep(G) forGa 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$$ {\mathcal{H}}^{\ast } $$ H . We discuss how ordinaryGorbifolds for finite groupsGare 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$$ \textrm{Rep}\left({\mathcal{H}}_8\right) $$ Rep H 8 , and discuss applications inc= 1 CFTs. We also discuss decomposition in the special case that the entire noninvertible symmetry group acts trivially.  more » « less
Award ID(s):
2310588 2014086
PAR ID:
10513510
Author(s) / Creator(s):
; ; ; ;
Publisher / Repository:
Journal of High Energy Physics
Date Published:
Journal Name:
Journal of High Energy Physics
Volume:
2024
Issue:
2
ISSN:
1029-8479
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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