An application of Cubical Cohomology to Adinkras and Supersymmetry Representations

TL;DR

This paper explores the use of cubical cohomology to analyze Adinkras, a class of graphs encoding supersymmetry representations, drawing analogies to characteristic classes on manifolds.

Contribution

It introduces a novel application of cubical cohomology to Adinkras, linking graph markings to cohomological concepts in supersymmetry.

Findings

Cochains on Adinkras correspond to vertex and edge markings.

Cohomological methods reveal structural properties of supersymmetry representations.

Analogies to characteristic classes provide new insights into Adinkra topology.

Abstract

An Adinkra is a class of graphs with certain signs marking its vertices and edges, which encodes off-shell representations of the super Poincar\'e algebra. The markings on the vertices and edges of an Adinkra are cochains for cubical cohomology. This article explores the cubical cohomology of Adinkras, treating these markings analogously to characteristic classes on smooth manifolds.