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.
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Samtleben, H., Wimmer, R. \( \mathcal{N} = 6 \) superspace constraints, SUSY enhancement and monopole operators. J. High Energ. Phys. 2010, 80 (2010). https://doi.org/10.1007/JHEP10(2010)080
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DOI: https://doi.org/10.1007/JHEP10(2010)080