Codimension-Two Defects and SYM on Orbifolds

TL;DR

This paper investigates $U(N)$ SYM theories on orbifold spaces by analyzing gauge theories with defects, revealing a geometric interpretation and computing partition functions on spaces with conical singularities.

Contribution

It introduces a novel approach linking gauge theories with defects to theories on branched covers, enabling partition function computations on singular spaces.

Findings

Partition functions computed on orbifold and conical singularity spaces.

Establishment of a relation between defects and branched cover theories.

Framework for analyzing multivalued fields via geometric interpretation.

Abstract

We study $U(N)$ SYM theories on spaces with orbifold singularities via an equivalent description in terms of gauge theories on smooth manifolds with insertions of Gukov-Witten and twist defects. The combined effect of the defects is to render the fields multivalued with respect to rotations around the support of the defects. This motivates a relation with theories on branched covers, for which the multivaluedness has a geometric interpretation. We compute the partition function of the theory with defects on a patch and use it as a building block to compute partition functions on several closed spaces with conical singularities.