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

In our investigation on quantum gravity, we introduce an infinite dimensional complex Lie algebra g(u) that extends e9. 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 Poincare 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.