Grassmann Variables in Jordan Matrix Models

TL;DR

This paper shows how Grassmann variables naturally emerge in Jordan matrix models using octonions, strengthening the link between supersymmetry and triality in theoretical physics.

Contribution

It introduces a novel way of deriving Grassmann variables within Jordan algebra-based matrix models, connecting supersymmetry and triality.

Findings

Grassmann variables emerge naturally in Jordan matrix models

Octonion algebra underpins the Grassmann algebra construction

Strengthens the theoretical link between supersymmetry and triality

Abstract

Here we demonstrate the emergence of Grassmann variables in matrix models based on the exceptional Jordan algebra. The Grassmann algebras are built naturally using the octonion algebra. We argue the appearance of Grassmann variables solidifies the relationship between supersymmetry and triality.