On non-minimal N=4 supermultiplets in 1D and their associated sigma-models

TL;DR

This paper constructs and classifies non-minimal N=4 supermultiplets in one dimension, explores their associated sigma-models, and discusses their implications for supersymmetry breaking.

Contribution

It introduces non-minimal linear representations of N=4 supersymmetry, analyzes their properties, and constructs two types of sigma-models based on these representations.

Findings

Classified inequivalent N=4 supermultiplets by graph connectivity.

Constructed off-shell sigma-models with different invariance properties.

Connected properties influence the form of supersymmetric actions.

Abstract

We construct the non-minimal linear representations of the N=4 Extended Supersymmetry in one-dimension. They act on 8 bosonic and 8 fermionic fields. Inequivalent representations are specified by the mass-dimension of the fields and the connectivity of the associated graphs. The oxidation to minimal N=5 linear representations is given. Two types of N=4 sigma-models based on non-minimal representations are obtained: the resulting off-shell actions are either manifestly invariant or depend on a constrained prepotential. The connectivity properties of the graphs play a decisive role in discriminating inequivalent actions. These results find application in partial breaking of supersymmetric theories.