Construction and classification of novel BPS Wilson loops in quiver Chern-Simons-matter theories

TL;DR

This paper constructs and classifies new BPS Wilson loops in various supersymmetric Chern-Simons-matter theories, revealing supersymmetry enhancements and their potential for exact calculations of vacuum expectation values.

Contribution

It introduces four classes of DT type BPS Wilson loops in multiple theories, with supersymmetry enhancements at specific parameters, and shows their relation to GY type loops via Q-exactness.

Findings

Four classes of Wilson loops preserving same supersymmetries as GY loops.

Supersymmetry enhancements occur at special parameter values.

Differences between DT and GY loops are Q-exact.

Abstract

In this paper we construct and classify novel Drukker-Trancanelli (DT) type BPS Wilson loops along infinite straight lines and circles in $\mathcal N=2,3$ quiver superconformal Chern-Simons-matter theories, Aharony-Bergman-Jafferis-Maldacena (ABJM) theory, and $\mathcal N=4$ orbifold ABJM theory. Generally we have four classes of Wilson loops, and all of them preserve the same supersymmetries as the BPS Gaiotto-Yin (GY) type Wilson loops. There are several free complex parameters in the DT type BPS Wilson loops, and for two classes of Wilson loops in ABJM theory and $\mathcal N=4$ orbifold ABJM theory there are supersymmetry enhancements at special values of the parameters. We check that the differences of the DT type and GY type Wilson loops are $Q$-exact with $Q$ being some supercharges preserved by both the DT type and GY type Wilson loops. The results would be useful to calculate vacuum expectation values of the DT type Wilson loops in matrix models if they are still BPS quantum mechanically.