Communications in Mathematical Physics

, Volume 298, Issue 2, pp 419-436

First online:

There is No “Theory of Everything” Inside E8

  • Jacques DistlerAffiliated withTheory Group, Department of Physics, and Texas Cosmology Center, University of Texas
  • , Skip GaribaldiAffiliated withDepartment of Mathematics & Computer Science, 400 Dowman Dr., Emory University Email author 

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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.