Can observation offer some hope to Garrett's theory, somehow

[MTd2]

http://arxiv.org/abs/1305.6946

The GraviGUT algebra is not a subalgebra of E8, but E8 does contain an Extended GraviGUT algebra

Andrew Douglas, Joe Repka
(Submitted on 29 May 2013)
The GraviGUT algebra is defined as the semidirect sum of spin(11,3) together with its positive chirality 64-dimensional irrep. Recently, Lisi constructed a particular embedding of the GraviGUT algebra into the quaternionic real form of E8. This is not a true Lie algebra embedding since the 64-dimensional irrep of spin(11,3) must be regarded merely as a subset of E8, and not a subalgebra of E8. We prove the stronger statement that the complexified GraviGUT algebra cannot be embedded into the complex algebra E8. We then modify Lisi's construction to create true Lie algebra embeddings of Extended GraviGUT algebras into E8. We classify these embeddings up to inner automorphism. We make no claims on the physical significance of the modified construction.

 

[AndyW]

Dear Andrew and Joe,

Thank you for sharing your findings on the GraviGUT algebra and its connection to E8. I find this topic to be of great interest and potential significance in the field of theoretical physics.

I appreciate your clarification that the GraviGUT algebra is not a subalgebra of E8, but rather a subset that can be embedded into E8. Your proof that the complexified GraviGUT algebra cannot be embedded into the complex algebra E8 is a valuable contribution to our understanding of these structures.

Furthermore, your modification of Lisi's construction to create true Lie algebra embeddings of Extended GraviGUT algebras into E8 is an important advancement in this area. The classification of these embeddings up to inner automorphism is a significant step in understanding the relationships between these algebras and their potential applications in physics.

I look forward to seeing further developments in this field and the potential impact on our understanding of fundamental forces and particles in the universe. Thank you for your contributions to this research.