Conformal Field Theories with Sporadic Group Symmetry

Jeff Harvey (Chicago)

Title: Conformal Field Theories with Sporadic Group Symmetry


Abstract: This seminar will be based on joint work with Jin-Beom Bae, Kimyeong Lee and Brandon Rayhaun. The Monster VOA/CFT has a c=24 stress tensor, but it also possesses many stress tensors or conformal vectors of lower central charge. For example, it contains 48 commuting c=1/2 conformal vectors. This allows one to decompose the Monster VOA into subVOAs that possess sporadic automorphism groups for a number of the sporadic groups that appear as subquotients of the Monster. A number of techniques are used to compute conjectured characters of these VOAs including Hecke operators for rational conformal field theories, modular linear differential equations and Rademacher sums. Many of the examples we find are connected to McKay's $\hat E_8$ correspondence for the Monster VOA.


Recording taken from the Arithmetic Geometry and Quantum Field Theory seminar, organised by Jeff Harvey and Minhyong Kim