| Summary: | 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.
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