Global Form of Flavor Symmetry Groups in 4d N=2 Theories of Class S

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.

arXiv comment46 pages; v2: Changed some previously confusing notation to improve clarity; v3: Added a glossary of notation, Added more computational details in the example labeled 'Bifundamental hyper' to illustrate other similar computations in the rest of the paper

References in corpus (21)

• Generalized Global Symmetries
• N=2 dualities
• Gauge Theories and Macdonald Polynomials
• An N=2 Superconformal Fixed Point with E_6 Global Symmetry
• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• Nilpotent orbits and codimension-two defects of 6d N=(2,0) theories
• Tinkertoys for Gaiotto Duality
• The Hilbert Series of the One Instanton Moduli Space
• Tinkertoys for the D_N series
• The Superconformal Index of the E_6 SCFT
• The Global Form of Flavor Symmetries and 2-Group Symmetries in 5d SCFTs
• On S-duality of 5d super Yang-Mills on S^1
• Tinkertoys for the Twisted D-Series
• Gaiotto Duality for the Twisted A_{2N-1} Series
• N=2 S-duality via Outer-automorphism Twists
• Tinkertoys for the E7 Theory
• Argyres-Douglas Theories in Class S Without Irregularity
• A Family of $4D$ $\mathcal{N}=2$ Interacting SCFTs from the Twisted $A_{2N}$ Series
• Tinkertoys for the Twisted $E_6$ Theory
• Tinkertoys for the $E_8$ Theory
• Distinquishing 4d N=2 SCFTs

Cited by in corpus (15)

• The Global Form of Flavor Symmetries and 2-Group Symmetries in 5d SCFTs
• Non-invertible Symmetries of Class $\mathcal{S}$ Theories
• 2-Group Symmetries in Class S
• Higher Symmetries of 5d Orbifold SCFTs
• 0-Form, 1-Form and 2-Group Symmetries via Cutting and Gluing of Orbifolds
• Mixed Anomalies, Two-groups, Non-Invertible Symmetries, and 3d Superconformal Indices
• Relative Defects in Relative Theories: Trapped Higher-Form Symmetries and Irregular Punctures in Class S
• 6d SCFTs, Center-Flavor Symmetries, and Stiefel--Whitney Compactifications
• Anomalies of Generalized Symmetries from Solitonic Defects
• Disconnected 0-Form and 2-Group Symmetries
• Higgs, Coulomb, and Hall-Littlewood
• Generalized Symmetries and Anomalies of 3d N=4 SCFTs
• A tale of 2-groups: D${}_p$(USp(2N)) theories
• Isomorphisms of 4d N=2 SCFTs from 6d
• Aspects of 4d supersymmetric dynamics and geometry