Codimension-Two Defects and SYM on Orbifolds

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.