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Defect groups of class $\mathcal{S}$ theories from the Coulomb branch
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abstract
We study the global forms of class $\mathcal{S}[A_{N-1}]$ 4d $\mathcal{N} = 2$ theories by deriving their defect groups (charges of line operators up to screening by local operators) from Coulomb branch data. Specifically, we employ an explicit construction of the BPS quiver for the case of full regular punctures to show that the defect group is $(\mathbb{Z}_N)^{2g}$, where $g$ is the genus of the associated Riemann surface. This determines a sector of surface operators in the 5d symmetry TFT. We show how these can also be identified from dimensional reduction of M-theory. We discuss connections to the theory of cluster algebras.
Forward citations
Cited by 2 Pith papers
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Topological Twisting of 4d $\mathcal{N}=2$ Supersymmetric Field Theories
For any 4d N=2 theory, topologically twisted partition functions depend on the diffeomorphism type, 't Hooft fluxes, and a generalized spin-c structure.
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SymTFTs and Non-Invertible Symmetries of 6d (2,0) SCFTs of Type $D$ from M-theory
The 7d SymTFT for 6d (2,0) D_N SCFTs is derived from M-theory on AdS7 × RP4, including the outer-automorphism Z2 sector, and is used to derive non-invertible symmetries and anomaly polynomials.
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