SUSY Equation Topology, Zonohedra, and the Search for Alternate Off-Shell Adinkras

TL;DR

This paper explores alternative topologies beyond hypercubes, such as zonohedra, to construct adinkra-like graphs and equations, revealing new structures that resemble supersymmetric systems but do not fully realize off-shell supersymmetry.

Contribution

It introduces a novel approach using zonohedra topologies to generate adinkra-like equations, expanding the understanding of supersymmetric graph structures.

Findings

Zonohedra can be used to construct adinkra-like graphs.

The resulting equations resemble supersymmetric systems.

These equations do not correspond to off-shell supersymmetry.

Abstract

Results are given from a search to form adinkra-like equations based on topologies that are not hypercubes. An alternate class of zonohedra topologies are used to construct adinkra-like graphs. In particular, the rhombic dodecahedron and rhombic icosahedron are studied in detail. Using these topological skeletons, equations similar to those of a supersymmetric system are found. But these fail to have the interpretation of an off-shell supersymmetric system of equations.