Exact results for supersymmetric abelian vortex loops in 2+1 dimensions

TL;DR

This paper introduces a class of supersymmetric defect loop operators in 2+1 dimensional N=2 gauge theories, providing exact expectation values via localization and exploring their role in IR dualities and SL(2,Z) transformations.

Contribution

It defines supersymmetric abelian vortex loop operators, offers a localization-based method for their exact expectation values, and analyzes their transformation properties under dualities.

Findings

Exact expectation values computed for supersymmetric vortex loops.

Demonstrated the role of defect loops in IR dualities.

Analyzed transformation properties under SL(2,Z) actions.

Abstract

We define a class of supersymmetric defect loop operators in N = 2 gauge theories in 2+1 dimensions. We give a prescription for computing the expectation value of such operators in a generic N = 2 theory on the three-sphere using localization. We elucidate the role of defect loop operators in IR dualities of supersymmetric gauge theories, and write down their transformation properties under the SL(2, Z) action on conformal theories with abelian global symmetries.