A Lorentz Covariant Holoraumy-Induced "Gadget" From Minimal Off-Shell 4D, N = 1 Supermultiplets

TL;DR

This paper introduces a Lorentz covariant 'gadget' metric on 4D, N=1 supermultiplet representation space, linking it to 1D adinkra network metrics, advancing understanding of supersymmetric structures.

Contribution

It constructs a new Lorentz covariant metric ('gadget') on 4D supermultiplet representations, connecting higher-dimensional supersymmetry to 1D adinkra network metrics.

Findings

Established a direct correspondence between 4D supermultiplet metrics and 1D adinkra network metrics.

Demonstrated the existence of a Lorentz covariant 'gadget' within minimal off-shell supermultiplets.

Provided a framework for analyzing supersymmetric representations via geometric metrics.

Abstract

Starting from three minimal off-shell 4D, $\cal N$ = 1 supermultiplets, using constructions solely defined within the confines of the four dimensional field theory we show the existence of a "gadget" - a member of a class of metrics on the representation space of the supermultiplets - whose values directly and completely correspond to the values of a metric defined on the 1d, $N$ = 4 adinkra networks adjacency matrices corresponding to the projections of the four dimensional supermultiplets.