Cosmological constant, supersymmetry, nonassociativity, and Big Numbers

TL;DR

This paper explores a nonassociative extension of supersymmetry, linking the associator coefficient to cosmological and particle physics scales, and discusses its implications for the smallness of fundamental constants.

Contribution

It introduces a nonassociative framework for supersymmetry and connects the associator coefficient to cosmological constant and electron radius scales.

Findings

Associator coefficient scales with Planck's constant and a characteristic length.

For cosmological constant scale, the scaled constant is about 10^{-120}.

For electron radius scale, the scaled constant is about 10^{-30}.

Abstract

The nonassociative generalization of supersymmetry is considered. It is shown that the associator of four supersymmetry generators has the coefficient $\sim \hbar/ \ell_0^2$ where $\ell_0$ is some characteristic length. Two cases are considered: (a) $\ell_0^{-2}$ coincides with the cosmological constant; (b) $\ell_0$ is the classical radius of electron. It is also shown that the scaled constant is of the order of $10^{-120}$ for the first case and $10^{-30}$ for the second case. The possible manifestation and smallness of nonassociativity is discussed.