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 AdS 4 × 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 ).

SUSY gauge theories on squashed three-spheres

“…In particular, in [3] it has been argued that the 3D partition function can be used to determine the superconformal R-symmetry at the infrared fixed points, in a similar spirit to a-maximization in 4D gauge theories. It has also been attracting wide attention from various other fields, for example Wilson loops [5,6], 3D dualities [2], large-N duality of topological string [7] and the ABJM theory at strong coupling [8,9,10]. The localization technique can also be applied to the theory on S 2 × S 1 and allows one to compute the superconformal index.…”

Notes on SUSY gauge theories on three-sphere

“…The techniques developed there have been applied to further studies of various topics, such as Wilson loops [6,7], 3D dualities [8] and large-N duality of topological string [9]. It has also been applied to the study of the ABJM theory at strong coupling, in particular its conjectured O(N 3/2 ) growth of the degrees of freedom [10,11,12]. Another application has recently been made to the study of domain walls in 4D N = 2 gauge theories [13,14] in connection with the AGT relation.…”

1/2-BPS Wilson loops and vortices in ABJM model

“…The very 1/2-BPS Wilson line operator of N = 6 Chern-Simons theory has been constructed recently in [8]. It turns out that the operator has some interesting and novel features.…”