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arXiv · 1609.01281

Punctures for Theories of Class $\mathcal{S}_Γ$

Jonathan J. Heckman·Patrick Jefferson·Tom Rudelius·Cumrun Vafa
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Abstract

With the aim of understanding compactifications of 6D superconformal field theories to four dimensions, we study punctures for theories of class $\mathcal{S}_Γ$. The class $\mathcal{S}_Γ$ theories arise from M5-branes probing $\mathbb{C}^2 / Γ$, an ADE singularity. The resulting 4D theories descend from compactification on Riemann surfaces decorated with punctures. We show that for class $\mathcal{S}_Γ$ 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 $\mathfrak{su}(2)$ generalizes in this broader context.

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Jonathan J. Heckman, Patrick Jefferson, Tom Rudelius, Cumrun Vafa. 2016-09-05. Punctures for Theories of Class $\mathcal{S}_Γ$. https://doi.org/10.1007/jhep03(2017)171

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