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2-Group Symmetries in Class S
by Lakshya Bhardwaj
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Submission summary
Authors (as registered SciPost users): | Lakshya Bhardwaj |
Submission information | |
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Preprint Link: | https://arxiv.org/abs/2107.06816v1 (pdf) |
Date accepted: | April 25, 2022 |
Date submitted: | Jan. 2, 2022, 3:39 p.m. |
Submitted by: | Bhardwaj, Lakshya |
Submitted to: | SciPost Physics |
Ontological classification | |
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Academic field: | Physics |
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Abstract
2-group symmetries are generalized symmetries that arise when 1-form and 0-form symmetries mix with each other. We uncover the existence of a class of 2-group symmetries in general 4d N=2 theories of Class S that can be constructed by compactifying 6d N=(2,0) SCFTs on Riemann surfaces carrying arbitrary regular punctures and outer-automorphism twist lines. The 2-group structure can be captured in terms of equivalence classes of line defects plus flavor Wilson lines, which can be thought of as accounting for screening of line defects while keeping track of flavor charges. We describe a method for computing these equivalence classes for a general Class S theory using the data on the Riemman surface used for compactifying its parent 6d N=(2,0) theory.
Published as SciPost Phys. 12, 152 (2022)
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2022-4-13 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2107.06816v1, delivered 2022-04-13, doi: 10.21468/SciPost.Report.4919
Strengths
1) Very clear discussion of generalities of 2-group symmetries
2) A nice algorithm to determine 2-group structure of class ${\cal S }$ theories
Weaknesses
Report
This paper is very well written. It is on a very topical subject of understanding higher group and higher form symmetries of general SCFTs. In particular it makes interesting use of geometric constructions of such theories. I think the result of this paper will be interesting to many researchers working in the field. I thus recommend it for publication in SciPost.
Report #1 by Anonymous (Referee 1) on 2022-2-5 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2107.06816v1, delivered 2022-02-05, doi: 10.21468/SciPost.Report.4324
Report
The key observation is that if the local junction operators are charged under a 0-form flavor symmetry, the 0- and 1-form symmetries can have non-trivial interplay, giving rise to a 2-group. The goal then becomes to identify the flavor charges of the local operators. This is again possible from examination of the Riemann surface—schematically, when the 2-chains giving the local junction operator pass over a puncture, the corresponding 4d local operator will be charged under the flavor symmetry associated with that puncture.
Altogether, this paper is insightful and very clearly written. In addition, the rather technical discussion in Section 4 is complimented with a beautifully explicit example in Section 5. For these reasons, I recommend this paper for publication in SciPost.
Requested changes
One very minor correction: above (2.19), I believe "2-form symmetry” should be “2-group symmetry”. Also, I think that the equality in (2.19) should actually be $\neq$?