Defect groups of class $\mathcal{S}$ theories from the Coulomb branch

• URL: http://arxiv.org/abs/2311.16224v3
• Date: Tue, 17 Dec 2024 14:54:55 GMT
• Title: Defect groups of class $\mathcal{S}$ theories from the Coulomb branch
• Authors: Elias Riedel Gårding,
• Abstract summary: We study the global forms of class $mathcalS[A_N-1]$ 4d $mathcalN = 2$ theories by deriving their defect groups from Coulomb branch data. We employ an explicit construction of the BPS quiver for the case of full regular punctures to show that the defect group is $(mathbbZ_N)2g$, where $g$ is the genus of the associated surface.
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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.

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