Authors: Carlos Castro
A candidate action for an Exceptional E8 gauge theory of gravity in 8D is constructed. It is obtained by recasting the E8 group as the semi-direct product of GL(8,R) with a deformed Weyl-Heisenberg group associated with canonical-conjugate pairs of vectorial and antisymmetric tensorial generators of rank two and three. Other actions are proposed, like the quartic E8 group-invariant action in 8D associated with the Chern-Simons E8 gauge theory defined on the 7-dim boundary of a 8D bulk. To finalize, it is shown how the E8 gauge theory of gravity can be embedded into a more general extended gravitational theory in Clifford spaces associated with the Cl(16) algebra and providing a solid geometrical program of a grand-unification of gravity with Yang-Mills theories. The key question remains if this novel gravitational model based on gauging the E8 group may still be renormalizable without spoiling unitarity at the quantum level.
Comments: 22 pages, This article will appear in the Int J. Geom. Meth in Mod Phys vol 6 , no. 6 (Sept 2009)
[v1] 25 Aug 2009
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