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arXiv · 2012.10248

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

Piero Truini·Alessio Marrani·Michael Rios·Klee Irwin
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Abstract

In our investigation on quantum gravity, we introduce an infinite dimensional complex Lie algebra $\textbf{${\mathfrak g}_{\mathsf u}$}$ that extends $\mathbf{e_9}$. It is defined through a symmetric Cartan matrix of a rank 12 Borcherds algebra. We turn $\textbf{${\mathfrak g}_{\mathsf u}$}$ into a Lie superalgebra $\textbf{$\mathfrak {sg}_{\mathsf u}$}$ with no superpartners, in order to comply with the Pauli exclusion principle. There is a natural action of the Poincar\'e group on $\textbf{$\mathfrak {sg}_{\mathsf u}$}$, which is an automorphism in the massive sector. We introduce a mechanism for scattering that includes decays as particular {\it resonant scattering}. Finally, we complete the model by merging the local $\textbf{$\mathfrak {sg}_{\mathsf u}$}$ into a vertex-type algebra.

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Piero Truini, Alessio Marrani, Michael Rios, Klee Irwin. 2020-12-18. Space, Matter and Interactions in a Quantum Early Universe. Part II : Superalgebras and Vertex Algebras. https://arxiv.org/abs/2012.10248

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