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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
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
Academic field: Physics
Specialties:
  • High-Energy Physics - Theory
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)


Reports on this Submission

Anonymous Report 1 on 2022-4-21 (Invited Report)

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In the new version of the preprint, the author has addressed the comments of the referees satisfactorily. The referee recommends the article for publication.

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