Chiral algebras of class S

Abstract: Four-dimensional N$$ \mathcal{N} $$ = 2 superconformal field theories have families of protected correlation functions that possess the structure of two-dimensional chiral algebras. In this paper, we explore the chiral algebras that arise in this manner in the context of theories of class S$$ \mathcal{S} $$. The class S$$ \mathcal{S} $$ duality web implies nontrivial associativity properties for the corresponding chiral algebras, the structure of which is best summarized in the language of generalized topological quantum field theory. We make a number of conjectures regarding the chiral algebras associated to various strongly coupled fixed points.