Notes on hyperloops in N=4 Chern-Simons-matter theories

TL;DR

This paper introduces new classes of circular Wilson loops in three-dimensional N=4 quiver Chern-Simons-matter theories on S^3, expanding the known operators by deforming existing BPS loops and incorporating superconnections.

Contribution

It constructs and classifies a new family of Wilson loop operators in N=4 Chern-Simons-matter theories, revealing their moduli spaces and dependence on discrete and continuous parameters.

Findings

New Wilson loop operators based on deformations of 1/4 BPS loops.

Classification of loops depending on discrete data and parameters.

Moduli spaces are conical manifolds similar to the conifold.

Abstract

We present new circular Wilson loops in three-dimensional N=4 quiver Chern-Simons-matter theory on S^3. At any given node of the quiver, a two-parameter family of operators can be obtained by opportunely deforming the 1/4 BPS Gaiotto-Yin loop. Including then adjacent nodes, the coupling to the bifundamental matter fields allows to enlarge this family and to construct loop operators based on superconnections. We discuss their classification, which depends on both discrete data and continuous parameters subject to an identification. The resulting moduli spaces are conical manifolds, similar to the conifold of the 1/6 BPS loops of the ABJ(M) theory.