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A<sc>bstract</sc> In this paper we discuss gauging noninvertible zero-form symmetries in two dimensions, extending our previous work. Specifically, in this work we discuss more general gauged noninvertible symmetries in which the noninvertible symmetry is not multiplicity free, and discuss the case of Rep(A4) in detail. We realize Rep(A4) gaugings for thec= 1 CFT at the exceptional point in the moduli space and find new self-duality under gauging a certain non-group algebra object, leading to a larger noninvertible symmetry Rep(SL(2, ℤ3)). We also discuss more general examples of decomposition in two-dimensional gauge theories with trivially-acting gauged noninvertible symmetries.
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Undoing decomposition
In this paper we discuss gauging one-form symmetries in two-dimensional theories. The existence of a global one-form symmetry in two dimensions typically signals a violation of cluster decomposition — an issue resolved by the observation that such theories decompose into disjoint unions, a result that has been applied to, for example, Gromov–Witten theory and gauged linear sigma model phases. In this paper we describe how gauging one-form symmetries in two-dimensional theories can be used to select particular elements of that disjoint union, effectively undoing decomposition. We examine such gaugings explicitly in examples involving orbifolds, nonsupersymmetric pure Yang–Mills theories, and supersymmetric gauge theories in two dimensions. Along the way, we learn explicit concrete details of the topological configurations that path integrals sum over when gauging a one-form symmetry, and we also uncover “hidden” one-form symmetries.
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- Award ID(s):
- 1720321
- PAR ID:
- 10147601
- Date Published:
- Journal Name:
- International Journal of Modern Physics A
- Volume:
- 34
- Issue:
- 35
- ISSN:
- 0217-751X
- Page Range / eLocation ID:
- 1950233
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.1142/S0217751X19502336
