Punctures for Theories of Class $\mathcal{S}_\Gamma$

Understand

With the aim of understanding compactifications of 6D superconformal field theories to four dimensions, we study punctures for theories of class $\mathcal{S}_{\Gamma}$.

• The class $\mathcal{S}_{\Gamma}$ theories arise from M5-branes probing $\mathbb{C}^2 / \Gamma$, an ADE singularity.
• The resulting 4D theories descend from compactification on Riemann surfaces decorated with punctures.
• We show that for class $\mathcal{S}_{\Gamma}$ 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.