Supersymmetric Wilson loops in N=4 super Chern-Simons-matter theory

TL;DR

This paper constructs and analyzes supersymmetric Wilson loops in a specific 3D super Chern-Simons-matter theory, demonstrating their properties and dualities, and establishing a foundation for exact calculations via localization.

Contribution

It introduces 1/4 and 1/2 BPS Wilson loops in N=4 super Chern-Simons-matter theory derived from orbifolded ABJM, proving their Q-exact difference and exploring their M-theory duals.

Findings

Constructed 1/4 and 1/2 BPS Wilson loops in the theory.

Proved the difference between these loops is Q-exact.

Analyzed the M-theory dual of the 1/2 BPS Wilson loop.

Abstract

We investigate the supersymmetric Wilson loops in $d=3$ $\mathcal{N}=4$ super Chern-Simons-matter theory obtained from non-chiral orbifold of ABJM theory. We work in both Minkowski spacetime and Euclidean space, and we construct 1/4 and 1/2 BPS Wilson loops. We also provide a complete proof that the difference between 1/4 and 1/2 Wilson loops is $Q$-exact with $Q$ being some supercharge that is preserved by both the 1/4 and 1/2 Wilson loops. This plays an important role in applying the localization techniques to compute the vacuum expectation values of Wilson loops. We also study the M-theory dual of the 1/2 BPS circular Wilson loop.