Abstract:

In 2013, Beem-Lemos-Liendo-Peelaers-Rastelli-van Rees constructed a correspondence between four dimensional N=2 SCFTs, a certain kind of supersymmetric quantum field theory, and vertex algebras. When applied to the theories of class S, one obtains a rich family of vertex algebras which furnish novel representations of critical level, affine Kac-Moody algebras. Moreover, these vertex algebras satisfy an intricate set of gluing relations, arising from the geometric origins of class S.

I will review a construction of this family, due to Arakawa. Then I will explain an extension of this work to the setting of twisted class S, where modules of two different affine Kac-Moody algebras are sewn together. This talk is based on joint work with Christopher Beem.