New BPS Wilson loops in $\mathcal N \textbf{= 4}$ circular quiver Chern-Simons-matter theories

TL;DR

This paper introduces new 1/4 BPS Wilson loops in three-dimensional $ ext{SCSM}$ theories, which are constructed as superconnections with non-trivial couplings, extending the known operators and enabling exact calculations.

Contribution

The authors construct novel 1/4 BPS Wilson loops in $ ext{SCSM}$ theories that cannot be reduced to previous block-diagonal forms, broadening the class of exactly computable operators.

Findings

New families of Wilson loops with non-trivial superconnections

Recovery of known loops at special couplings

Identification of gravity duals in orbifold ABJM theory

Abstract

We construct new families of 1/4 BPS Wilson loops in circular quiver $\mathcal N=4$ superconformal Chern-Simons-matter (SCSM) theories in three dimensions. They are defined as the holonomy of superconnections that contain non-trivial couplings to scalar and fermions, and cannot be reduced to block-diagonal matrices. Consequently, the new operators cannot be written in terms of double-node Wilson loops, as the ones considered so far in the literature. For particular values of the couplings the superconnection becomes block-diagonal and we recover the known fermionic 1/4 and 1/2 BPS Wilson loops. The new operators are cohomologically equivalent to bosonic 1/4 BPS Wilson loops and are then amenable of exact evaluation via localization techniques. Moreover, in the case of orbifold ABJM theory we identify the corresponding gravity duals for some of the 1/4 and 1/2 BPS Wilson loops.