Deformed N=1 supersymmetry

TL;DR

This paper explores a deformation of N=1 superspace where the odd coordinates do not anticommute, modifies the algebraic relations, and finds that standard supersymmetric theories remain compatible with this deformation.

Contribution

It introduces a new deformation of N=1 superspace with non-anticommuting coordinates and demonstrates compatibility with existing supersymmetric field theories.

Findings

Superspace coordinates' (anti)commutation relations are modified.

Supersymmetric and associative star product is defined.

Standard N=1 supersymmetric theories are compatible with the deformation.

Abstract

We consider a deformation of N=1 four dimensional Minkowski superspace where odd coordinates $\theta^{\alpha}$ do not anticommute. We define supersymmetric and associative star product and show how the remaining (anti)commutation relations among the superspace coordinates are modified. In particular, the even coordinates do not commute as well. We also study chiral and vector superfields and their interactions. Suprisingly we find that ordinary undeformed N=1 supersymmetric field theories are compatible with the deformed supersymmetry considered.