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 $$\sim $$ $$\hbar /{l_0^2}$$ where $$l_0$$ is some characteristic length. Two cases are considered: (a) $$l_0^{-2}$$ coincides with the cosmological constant; (b) $$l_0$$ is the classical radius of the 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.