Orbifolds, defects and sphere partition function

Gauge theories in the presence of codimension two vortex defects are known to be related to the theories on orbifolds. by using this relation we study the localized path integrals of 2d $$ mathcal{n}=left(2,2right) $$ susy gauge theories with point-like vortex defects. we present a formula for the correlation functions of vortex defects inserted at the north and the south poles of squashed spheres. for abelian gauge theories the correlators are locally constant as functions of the parameters of the defect, but exhibit discontinuity at some threshold values determined from the r-charges of the matter multiplets. for non-abelian gauge groups the correlators depend non-trivially on the types of gauge symmetry breaking due to the defects.