A supermatrix model for N=6 super Chern-Simons-matter theory

TL;DR

This paper constructs a supersymmetric Wilson loop operator in N=6 super Chern-Simons-matter theory, showing it can be computed via a supermatrix model and relating it to supergroup Chern-Simons theory.

Contribution

It introduces a superconnection-based Wilson loop invariant under half the supercharges, applicable to any supergroup representation, and links the theory to a supermatrix model via localization.

Findings

Wilson loop couples to gauge, scalar, and fermion fields

Explicit formulas for loops along straight line and circle

Circular loop computed by a supermatrix model

Abstract

We construct the Wilson loop operator of N=6 super Chern-Simons-matter which is invariant under half of the supercharges of the theory and is dual to the simplest macroscopic open string in AdS_4 x CP^3. The Wilson loop couples, in addition to the gauge and scalar fields of the theory, also to the fermions in the bi-fundamental representation of the U(N) x U(M) gauge group. These ingredients are naturally combined into a superconnection whose holonomy gives the Wilson loop, which can be defined for any representation of the supergroup U(N|M). Explicit expressions for loops supported along an infinite straight line and along a circle are presented. Using the localization calculation of Kapustin et al. we show that the circular loop is computed by a supermatrix model and discuss the connection to pure Chern-Simons theory with supergroup U(N|M).