The generalized cusp in ABJ(M) N = 6 Super Chern-Simons theories

TL;DR

This paper introduces a new class of supersymmetric Wilson loops in ABJ(M) theories, analyzing their properties and computing their expectation values at two loops to understand particle interactions.

Contribution

It constructs a generalized cusped Wilson loop in N=6 super Chern-Simons theories, extending previous configurations and providing explicit two-loop calculations.

Findings

Explicit two-loop expectation value for the generalized cusp

Identification of the interaction potential between BPS particles

Connection to localization and integrability in three dimensions

Abstract

We construct a generalized cusped Wilson loop operator in N = 6 super Chern-Simons-matter theories which is locally invariant under half of the supercharges. It depends on two parameters and interpolates smoothly between the 1/2 BPS line or circle and a pair of antiparallel lines, representing a natural generalization of the quark-antiquark potential in ABJ(M) theories. For particular choices of the parameters we obtain 1/6 BPS configurations that, mapped on S^2 by a conformal transformation, realize a three-dimensional analogue of the wedge DGRT Wilson loop of N = 4. The cusp couples, in addition to the gauge and scalar fields of the theory, also to the fermions in the bifundamental representation of the U(N)xU(M) gauge group and its expectation value is expressed as the holonomy of a suitable superconnection. We discuss the definition of these observables in terms of traces and the role of the boundary conditions of fermions along the loop. We perform a complete two-loop analysis, obtaining an explicit result for the generalized cusp at the second non-trivial order, from which we read off the interaction potential between heavy 1/2 BPS particles in the ABJ(M) model. Our results open the possibility to explore in the three-dimensional case the connection between localization properties and integrability, recently advocated in D = 4.