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

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 AdS4 ×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) × 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).