Three-point non-associative supersymmetry generalization

TL;DR

This paper explores a novel non-associative extension of supersymmetry using three-point associators, analyzing algebraic properties, dimensional aspects, and the potential physical implications of non-associativity.

Contribution

It introduces a three-point non-associative supersymmetry framework, calculates Jacobiators, and assesses the physical significance of non-associativity in this context.

Findings

Jacobiators can be zero with specific associator coefficients

Dimensional analysis constrains associator coefficients

Non-associativity is estimated to be very weak

Abstract

We consider a non-associative generalization of supersymmetry based on three-point associators like $\left[ Q_x, Q_y, Q_z \right]$ for $Q_{a, \dot a}$ supersymmetric generators. Such associators are connected with the products of $Q_{a, \dot a}$ and $x_{b \dot b}$. We: (a) calculate Jacobiators and show that the Jacobiators can be zero with some choice of corresponding coefficients in associators; (b) perform dimensional analysis for the coefficients in associators; (d) calculate some commutators involving coordinates and momentums; (e) estimate the weakness of non-associativity.