Chiral algebras of class S

TL;DR

This paper investigates the structure of two-dimensional chiral algebras emerging from four-dimensional N=2 superconformal theories of class S, revealing their complex duality relations and proposing new conjectures about their properties.

Contribution

It characterizes the chiral algebras associated with class S theories and explores their duality and associativity properties using generalized topological quantum field theory.

Findings

Chiral algebras encode protected correlation functions in class S theories.

Duality web implies nontrivial associativity in these chiral algebras.

Proposes conjectures for chiral algebras at strongly coupled fixed points.

Abstract

Four-dimensional 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. The class 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.