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1-form Symmetries of 4d N=2 Class S Theories
by Lakshya Bhardwaj, Max Hubner, Sakura Schafer-Nameki
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Submission summary
| Authors (as registered SciPost users): | Lakshya Bhardwaj |
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| Preprint Link: | https://arxiv.org/abs/2102.01693v2 (pdf) |
| Date accepted: | 2021-10-15 |
| Date submitted: | 2021-06-21 13:15 |
| Submitted by: | Bhardwaj, Lakshya |
| Submitted to: | SciPost Physics |
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| Academic field: | Physics |
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Abstract
We determine the 1-form symmetry group for any 4d N = 2 class S theory constructed by compactifying a 6d N=(2,0) SCFT on a Riemann surface with arbitrary regular untwisted and twisted punctures. The 6d theory has a group of mutually non-local dimension-2 surface operators, modulo screening. Compactifying these surface operators leads to a group of mutually non-local line operators in 4d, modulo screening and flavor charges. Complete specification of a 4d theory arising from such a compactification requires a choice of a maximal subgroup of mutually local line operators, and the 1-form symmetry group of the chosen 4d theory is identified as the Pontryagin dual of this maximal subgroup. We also comment on how to generalize our results to compactifications involving irregular punctures. Finally, to complement the analysis from 6d, we derive the 1-form symmetry from a Type IIB realization of class S theories.
Published as SciPost Phys. 11, 096 (2021)
Reports on this Submission
Report #1 by Anonymous (Referee 1) on 2021-7-16 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2102.01693v2, delivered 2021-07-16, doi: 10.21468/SciPost.Report.3247
Report
In this paper the authors study the 1-form symmetries present in 4d N=2 theories of class S. This is a fairly large class of N=2 theories in four dimensions arising from compactifying the (2,0) theories on Riemann surfaces with punctures. Particularly during the couple of years or so there have been a number of papers developing methods agnostic to the existence of a Lagrangian for determining the structure of generalised global symmetries in various theories. This paper is an important contribution to this effort.
The analysis is fairly thorough, and convincing. The proposed rules are natural, and they give the expected results in a large number of examples where the result can be computed via alternative methods. There is also a discussion on how to derive the same rules from a geometric perspective, which lends additional support to the proposed rules.
I see no issues with the content or the presentation of the paper, and the results are interesting and timely, so I recommend publication.