N = 6 superspace constraints, SUSY enhancement and monopole operators

Abstract

We present a systematic analysis of the N = 6 superspace constraints in three space-time dimensions. The general coupling between vector and scalar supermultiplets is encoded in an SU(4) tensor Wij which is a function of the matter fields and subject to a set of algebraic and super-differential relations. We give a genuine N = 6 classification for superconformal models with polynomial interactions and find the known ABJM and ABJ models. We further study the issue of supersymmetry enhancement to N = 8 and the role of monopole operators in this scenario. To this end we assume the existence of a composite monopole operator superfield which we use to formulate the additional supersymmetries as internal symmetries of the N = 6 superspace constraints. From the invariance conditions of these constraints we derive a system of superspace constraints for the proposed monopole operator superfield. This constraint system defines the composite monopole operator superfield analogously to the original N = 6 superspace constraints defining the dynamics of the elementary fields.