A network of hyperloops

TL;DR

This paper explores the space of BPS Wilson loops in 3D $ abla$-N=4 Chern-Simons-matter theory, discovering new moduli spaces of nonconformal BPS loops and analyzing their supersymmetric properties.

Contribution

It introduces an algorithm to classify BPS Wilson loops, revealing new moduli spaces and extending previous classifications in the literature.

Findings

Discovered new moduli spaces of nonconformal BPS Wilson loops.

Extended the classification of BPS Wilson loops to include new supersymmetric configurations.

The moduli spaces are closed under the proposed formalism.

Abstract

In this paper we complete the exploration of connected components of the space of BPS Wilson loops in three-dimensional $\mathcal{N}=4$ Chern-Simons-matter theory on $S^3$. The algorithm is to start with a supersymmetric Wilson loop, choose a preserved supercharge, and look for BPS deformations built out of the matter fields in the proper representations. Using this, we discover many new moduli spaces of nonconformal BPS Wilson loops preserving a single or two supercharges, which are subsets of the symmetries of the 1/4 and 3/8 BPS operators. Along with the those previously found in arXiv:2012.07096, arXiv:2206.07390 and arXiv:2210.03758, the total moduli spaces are closed under this formalism.