1/2-BPS Wilson Loops and Vortices in ABJM Model

TL;DR

This paper investigates the low-energy dynamics of 1/2-BPS Wilson loops in the ABJM model, revealing their structure as superconnections and their interpretation as vortices or strings, advancing understanding of supersymmetric gauge operators.

Contribution

It introduces a supergauge symmetry framework for 1/2-BPS Wilson loops in ABJM, explaining their supersymmetry invariance and vortex interpretation, which is a novel insight.

Findings

Wilson loops as holonomies of U(N|N) superconnections

Supersymmetry invariance via fermionic supergauge transformations

Identification of Wilson loops as 1/2-BPS vortices or strings

Abstract

We explore the low-energy dynamics of 1/2-BPS heavy particles coupled to the ABJM model via the Higgsing of M2-branes, with focus on physical understanding of the recently discovered 1/2-BPS Wilson loop operators. The low-energy theory of 1/2-BPS heavy particles turns out to have the U(N|N) supergauge symmetry, which explains the novel structure of the 1/2-BPS Wilson loop operator as a holonomy of a U(N|N) superconnection. We show that the supersymmetric transformation of the Wilson loop operator can be identified as a fermionic supergauge transformation, which leads to their invariance under half of the supersymmetry. We also argue that 1/2-BPS Wilson loop operators appear as 1/2-BPS vortices with vorticity 1/k. Such a vortex can be naturally interpreted as a membrane wrapping the Z_k cycle once, or type IIA fundamental string.