Localization and Duality for ABJM Latitude Wilson Loops

TL;DR

This paper studies BPS latitude Wilson loops in three-dimensional supersymmetric gauge theories, deriving a matrix model for ABJM and exploring their dualities and extensions to other theories.

Contribution

It derives a matrix model for latitude Wilson loops in ABJM via localization and extends the analysis to more general Chern-Simons-matter theories, also defining new loop operators.

Findings

Matrix model for ABJM latitude Wilson loop derived.

Extension of computations to general Chern-Simons-matter theories.

Identification of a dual bound state of Wilson and vortex loops.

Abstract

We investigate several aspects of BPS latitude Wilson loops in gauge theories in three dimensions with $\mathcal{N}\ge 4$ supersymmetry. We derive a matrix model for the bosonic latitude Wilson loop in ABJM using supersymmetric localization, and show how to extend the computation to more general Chern-Simons-matter theories. We then define latitude type Wilson and vortex loop operators in theories without Chern-Simons terms, and explore a connection to the recently derived superalgebra defining local Higgs and Coulomb branch operators in these theories. Finally, we identify a BPS loop operator dual to the bosonic latitude Wilson loop which is a novel bound state of Wilson and vortex loops, defined using a worldvolume supersymmetric quantum mechanics.