Piero Truini, Alessio Marrani, Michael Rios, Klee Irwin (2020)

In our investigation on quantum gravity, we introduce an infinite dimensional complex Lie algebra 𝔤𝗎 that extends e9. It is defined through a symmetric Cartan matrix of a rank 12 Borcherds algebra. We turn 𝔤𝗎 into a Lie superalgebra 𝔰𝔤𝗎 with no superpartners, in order to comply with the Pauli exclusion principle. There is a natural action of the Poincaré group on 𝔰𝔤𝗎, 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 𝔰𝔤𝗎 into a vertex-type algebra.