Factorized class $S$ theories and surface defects

TL;DR

This paper explores how certain class S theories can be decomposed into multiple independent 4D N=2 theories using surface defects, providing explicit constructions and checks for this factorization.

Contribution

It introduces a method to construct factorized class S theories via half-BPS surface defects and verifies the product structure of their Coulomb branches.

Findings

Successfully reproduces a known realization of two N=2 superconformal SU(2) QCD theories as a class S theory.

Provides explicit checks confirming the product structure of Coulomb branches in example theories.

Abstract

It is known that some theories of class $S$ are actually factorized into multiple decoupled nontrivial four-dimensional $N=2$ 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 $N=2$ superconformal $SU(2)$ QCD, describing this factorized theory as a class $S$ theory of type $A_3$ 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.