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We provide a systematic method to deduce the global form of flavor symmetrygroups in 4d N=2 theories obtained by compactifying 6d N=(2,0) superconformalfield theories (SCFTs) on a Riemann surface carrying regular punctures andpossibly outer-automorphism twist lines. Apriori, this method only determinesthe group associated to the manifest part of the flavor symmetry algebra, butoften this information is enough to determine the group associated to the fullenhanced flavor symmetry algebra. Such cases include some interesting andwell-studied 4d N=2 SCFTs like the Minahan-Nemeschansky theories. The symmetrygroups obtained via this method match with the symmetry groups obtained using aLagrangian description if such a description arises in some duality frame.Moreover, we check that the proposed symmetry groups are consistent with thesuperconformal indices available in the literature. As another application, ourmethod finds distinct global forms of flavor symmetry group for pairs ofinteracting 4d N=2 SCFTs (recently pointed out in the literature) whose Coulombbranch dimensions, flavor algebras and levels coincide (along with otherinvariants), but nonetheless are distinct SCFTs.

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