Conformal Field Theories with Sporadic Group Symmetry

The monster sporadic group is the automorphism of a central charge \(c=24\) vertex operator algebra (VOA) or meromorphic conformal field theory (CFT). In addition to its stress tensor T(z), this contains many other vectors smaller charge; for example, it admits 48 commuting \(c=\frac{1}{2}\) whose sum T(z). Such decompositions allow one construct new CFTs from CFT in manner analogous Goddard-Kent-Olive (GKO) coset method affine Lie algebras. We use procedure produce evidence existence number with symmetry groups and employ variety techniques, including Hecke operators, modular linear differential equations, Rademacher sums, compute characters these CFTs. Our examples include (extensions of) nine appearing as subquotients monster, well simple \({}^2{\textit{E}}_6(2)\) \({\textit{F}}_4(2)\) type. Many are naturally associated McKay’s \(\widehat{E_8}\) correspondence, we structure Norton’s monstralizer pairs more generally organize our presentation.