There is No ``Theory of Everything'' Inside E_{8}
Abstract
We analyze certain subgroups of real and complex forms of the Lie group E_{8}, 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 E_{8} lacks certain representationtheoretic 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.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 September 2010
 DOI:
 10.1007/s002200101006y
 arXiv:
 arXiv:0905.2658
 Bibcode:
 2010CMaPh.298..419D
 Keywords:

 Mathematics  Representation Theory;
 High Energy Physics  Theory;
 22E47 (Primary);
 17B25;
 81R05;
 83E15 (Secondary)
 EPrint:
 Final version, to appear in Communications in Mathematical Physics. The main difference, from the previous version, is the creation of a new section, containing a response to Lisi's objections to our work