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Higher-Matter and Landau-Ginzburg Theory of Higher-Group Symmetries
by Ruizhi Liu, Ran Luo, Yi-Nan Wang
Submission summary
| Authors (as registered SciPost users): | Yinan Wang |
| Submission information | |
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| Preprint Link: | scipost_202412_00041v1 (pdf) |
| Date submitted: | 2024-12-22 00:16 |
| Submitted by: | Wang, Yinan |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Higher-matter is defined by higher-representation of a symmetry algebra, such as the $p$-form symmetries, higher-group symmetries or higher-categorical symmetries. In this paper, we focus on the cases of higher-group symmetries, which are formulated in terms of the strictification of weak higher-groups. We systematically investigate higher-matter charged under 2-group symmetries, defined by automorphism 2-representations. Furthermore, we construct a Lagrangian formulation of such higher-matter fields coupled to 2-group gauge fields in the path space of the spacetime manifold. We interpret such model as the Landau-Ginzburg theory for 2-group symmetries, and discuss the spontaneous symmetry breaking (SSB) of 2-group symmetries under this framework. Examples of discrete and continuous 2-groups are discussed. Interestingly, we find that a non-split 2-group symmetry can admit an SSB to a split 2-group symmetry, where the Postnikov class is trivialized. We also briefly discuss the strictification of weak 3-groups, weak 3-group gauge fields and 3-representations in special cases.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
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- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
We would like to comment on the Referee #1's requested changes and the revisions on the draft:
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For the physical operators in the strict 2-group gauge theory, we provided a discussion of gauge invariant operators defined on a surface with boundary in the Section 4.3, which is already present in the previous version of draft.
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Regarding the faithfulness of strict 2-group description, we added a paragraph on page 4: "In a theory with 2-group global symmetry, the symmetry defects can be labeled by weak 2-group elements or by elements of the corresponding strict 2-group. For the latter case, the strict 2-group labeling is not faithful because the map from the strict 2-group to the corresponding weak 2-group description is not injective."
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We have followed the paper hep-th/0412325 in which the 2-group gauge theory is formulated on the path space, and we do not make distinction between a general path and a closed loop in the current paper.
Best regards, The authors
List of changes
1. We added a paragraph on page 4: "In a theory with 2-group global symmetry, the symmetry defects can be labeled by weak 2-group elements or by elements of the corresponding strict 2-group. For the latter case, the strict 2-group labeling is not faithful because the map from the strict 2-group to the corresponding weak 2-group description is not injective."
2. We added the reference Chen:2020msl