There is No “Theory of Everything” Inside E8

@article{Distler2009ThereIN,
  title={There is No “Theory of Everything” Inside E8},
  author={Jacques Distler and Skip Garibaldi},
  journal={Communications in Mathematical Physics},
  year={2009},
  volume={298},
  pages={419-436}
}
We analyze certain subgroups of real and complex forms of the Lie group E8, and deduce that any “Theory of Everything” obtained by embedding the gauge groups of gravity and the Standard Model into a real or complex form of E8 lacks certain representation-theoretic properties required by physical reality. The arguments themselves amount to representation theory of Lie algebras in the spirit of Dynkin’s classic papers and are written for mathematicians. 
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