Tinkertoys for the E7 Theory

Understand

We classify the class $S$ theories of type $E_7$.

• These are four-dimensional $\mathcal{N}=2$ superconformal field theories arising from the compactification of the $E_7$ $(2,0)$ theory on a punctured Riemann surface, $C$.
• The classification is given by listing all 3-punctured spheres ("fixtures"), and connecting cylinders, which can arise in a pants-decomposition of $C$.
• We find exactly 11,000 fixtures with three regular punctures, and an additional 48 with one "irregular puncture" (in the sense used in our previous works).