Space, Matter and Interactions in a Quantum Early Universe. Part II : Superalgebras and Vertex Algebras

Abstract

In our investigation on quantum gravity, we introduce an infinite dimensional complex Lie algebra g u that extends e 9 . It is defined through a symmetric Cartan matrix of a rank 12 Borcherds algebra. We turn g u into a Lie superalgebra sg u with no superpartners, in order to comply with the Pauli exclusion principle. There is a natural action of the Poincaré group on sg u , which is an automorphism in the massive sector. We introduce a mechanism for scattering that includes decays as particular resonant scattering. Finally, we complete the model by merging the local sg u into a vertex-type algebra.