$ \mathcal{N} = 6 $ superspace constraints, SUSY enhancement and monopole operators

Abstract

We present a systematic analysis of the $ \mathcal{N} = 6 $ superspace constraints in three space-time dimensions. The general coupling between vector and scalar supermultiplets is encoded in an SU(4) tensor Wj i which is a function of the matter fields and subject to a set of algebraic and super-differential relations. We give a genuine $ \mathcal{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 $ \mathcal{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 $ \mathcal{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 $ \mathcal{N} = 6 $ superspace constraints defining the dynamics of the elementary fields.