A network of hyperloops.

In this paper we complete the exploration of connected components of the space of BPS Wilson loops in three-dimensional N = 4 Chern-Simons-matter theory on S³. 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 [1-2] and [3], the total moduli spaces are closed under this formalism. [ABSTRACT FROM AUTHOR]