N=6 Superspace Constraints, SUSY Enhancement and Monopole Operators

TL;DR

This paper systematically analyzes N=6 superspace constraints in three dimensions, classifies superconformal models including ABJM and ABJ, and explores supersymmetry enhancement to N=8 via monopole operators.

Contribution

It provides a classification of N=6 superconformal models with polynomial interactions and introduces a framework for understanding supersymmetry enhancement through monopole operators.

Findings

Classified N=6 superconformal models including ABJM and ABJ.

Developed a superspace constraint system for monopole operators.

Proposed a mechanism for supersymmetry enhancement to N=8.

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 $W^i_j$ 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.