Factorized class S theories and surface defects

Abstract

Abstract It is known that some theories of class S are actually factorized into multiple decoupled nontrivial four-dimensional $$ \mathcal{N} $$ N = 2 theories. We propose a way of constructing examples of this phenomenon using the physics of half-BPS surface defects, and check that it works in one simple example: it correctly reproduces a known realization of two copies of $$ \mathcal{N} $$ N = 2 superconformal SU(2) QCD, describing this factorized theory as a class S theory of type A3 on a five-punctured sphere with a twist line. Separately, we also present explicit checks that the Coulomb branch of a putative factorized class S theory has the expected product structure, in two examples.