# On a $\mathbb{Z}_2^n$-Graded Version of Supersymmetry

## TL;DR

This paper generalizes superspace by incorporating $Z_2^n$-graded spinor coordinates, leading to a novel mathematical framework that extends super-Minkowski space with commuting, nilpotent spinors.

## Contribution

It introduces a $Z_2^n$-graded extension of superspace using $Z_2^n$-manifolds, providing a new formalism for supersymmetry with commuting nilpotent spinors.

## Key findings

- Develops a $Z_2^n$-graded super-Minkowski space framework
- Shows spinor coordinates are nilpotent and commute
- Provides a categorical approach to $Z_2^n$-graded superspaces

## Abstract

We extend the notion of super-Minkowski space-time to include $\mathbb{Z}_2^n$-graded (Majorana) spinor coordinates. Our choice of the grading leads to spinor coordinates that are nilpotent but commute amongst themselves. The mathematical framework we employ is the recently developed category of $\mathbb{Z}_2^n$-manifolds understood as locally ringed spaces. The formalism we present resembles $\mathcal{N}$-extended superspace (in the presence of central charges), but with some subtle differences due to the exotic nature of the grading employed.