Toward a Connection between the Oriented Matroid Theory and Supersymmetry

TL;DR

This paper explores a potential link between oriented matroid theory and supersymmetry, suggesting that Grassmann-Plucker relations serve as a common mathematical foundation, and proposes a mechanism to incorporate supersymmetry into matroid theory.

Contribution

It introduces a novel connection between oriented matroids and supersymmetry through Grassmann-Plucker relations and proposes a new method to implement supersymmetry within matroid theory.

Findings

Grassmann-Plucker relations appear in both oriented matroids and supergravity solutions.

A proposed mechanism uses phirotopes to incorporate supersymmetry into matroid theory.

Establishes a conceptual bridge between combinatorial geometry and high-energy physics.

Abstract

We considered the possibility that the oriented matroid theory is connected with supersymmetry via the Grassmann-Plucker relations. The main reason for this, is that such relations arise in both in the chirotopes definition of an oriented matroid, and in maximally supersymmetric solutions of eleven- and ten-dimensional supergravity theories. Taking this observation as a motivation, and using the concept of a phirotope, we propose a mechanism to implement supersymmetry in the context of the oriented matroid theory.