Cosmological constant, supersymmetry, nonassociativity, and Big Numbers

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.