Abstract
With the aim of understanding compactifications of 6D superconformal field theories to four dimensions, we study punctures for theories of class \( {\mathcal{S}}_{\varGamma } \). The class \( {\mathcal{S}}_{\varGamma } \) theories arise from M5-branes probing ℂ 2/Γ, an ADE singularity. The resulting 4D theories descend from compactification on Riemann surfaces decorated with punctures. We show that for class \( {\mathcal{S}}_{\varGamma } \) theories, a puncture is specified by singular boundary conditions for fields in the 5D quiver gauge theory obtained from compactification of the 6D theory on a cylinder geometry. We determine general boundary conditions and study in detail solutions with first order poles. This yields a generalization of the Nahm pole data present for 1/2 BPS punctures for theories of class \( \mathcal{S} \). Focusing on specific algebraic structures, we show how the standard discussion of nilpotent orbits and its connection to representations of \( \mathfrak{s}\mathfrak{u}(2) \) generalizes in this broader context.
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Heckman, J.J., Jefferson, P., Rudelius, T. et al. Punctures for theories of class \( {\mathcal{S}}_{\varGamma } \) . J. High Energ. Phys. 2017, 171 (2017). https://doi.org/10.1007/JHEP03(2017)171
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DOI: https://doi.org/10.1007/JHEP03(2017)171