Orbifolds, Defects and Sphere Partition Function

TL;DR

This paper explores the relationship between vortex defects in 2D SUSY gauge theories and orbifold theories, providing formulas for defect correlation functions on squashed spheres and analyzing their behavior for Abelian and non-Abelian groups.

Contribution

It introduces a new formula for vortex defect correlation functions on squashed spheres, linking gauge theories with orbifold descriptions and analyzing defect parameter effects.

Findings

Correlators are locally constant for Abelian theories but show discontinuities at certain thresholds.

Non-Abelian theories exhibit non-trivial dependence on gauge symmetry breaking due to defects.

The study reveals how defect parameters influence the correlation functions and their discontinuities.

Abstract

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 N=(2,2) 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 by the deficit angle at the poles and 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.