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Global Form of Flavor Symmetry Groups in 4d N=2 Theories of 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/2105.08730v3 (pdf) |
| Date accepted: | 2022-05-03 |
| Date submitted: | 2022-04-19 11:57 |
| Submitted by: | Bhardwaj, Lakshya |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We provide a systematic method to deduce the global form of flavor symmetry groups in 4d N=2 theories obtained by compactifying 6d N=(2,0) superconformal field theories (SCFTs) on a Riemann surface carrying regular punctures and possibly outer-automorphism twist lines. Apriori, this method only determines the group associated to the manifest part of the flavor symmetry algebra, but often this information is enough to determine the group associated to the full enhanced flavor symmetry algebra. Such cases include some interesting and well-studied 4d N=2 SCFTs like the Minahan-Nemeschansky theories. The symmetry groups obtained via this method match with the symmetry groups obtained using a Lagrangian description if such a description arises in some duality frame. Moreover, we check that the proposed symmetry groups are consistent with the superconformal indices available in the literature. As another application, our method finds distinct global forms of flavor symmetry group for pairs of interacting 4d N=2 SCFTs (recently pointed out in the literature) whose Coulomb branch dimensions, flavor algebras and levels coincide (along with other invariants), but nonetheless are distinct SCFTs.
List of changes
The following changes were made after referees' suggestions:
1. A glossary of notation is included as an appendix.
2. More details on computation were provided in the example labeled 'Bifundamental Hyper' in Section 4.1. The author hopes that this would act as a good illustration for carrying out similar computations in the rest of Section 4.
3. An explanation was added after equation (3.7) justifying why equation (3.7) does not have complex conjugates, but equation (3.4) does.
Published as SciPost Phys. 12, 183 (2022)