6D SCFTs and the Classification of Homomorphisms ΓADE→E8
Advances in Theoretical and Mathematical Physics
We elucidate the correspondence between a particular class of superconformal field theories in six dimensions and homomorphisms from discrete subgroups of SU(2) into E8, as predicted from string dualities. We show how this match works for homomorphisms from the binary icosahedral group SL(2,5) into E8, correcting previous errors in both the mathematics and physics literature. We use this correspondence to list the homomorphisms from binary dihedral groups, the binary tetrahedral group, and the binary octahedral group into E8 — a novel mathematical result. The partial ordering specified by renormalization group flows suggests an ordering on these homomorphisms similar to the known ordering of nilpotent orbits of a simple Lie algebra dictated by the Hasse diagram.
Frey, Darrin D. and Rudelius, Tom, "6D SCFTs and the Classification of Homomorphisms ΓADE→E8" (2020). Science and Mathematics Faculty Publications. 405.