## An Exceptional E_{8} Gauge Theory of Gravity in D = 8, Clifford Spaces and Grand Unification

**Authors:** Carlos Castro

A candidate action for an Exceptional E_{8} gauge theory of gravity in 8D
is constructed. It is obtained by recasting the E_{8} 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 E_{8} group-invariant action in 8D associated with the Chern-Simons
E_{8} gauge theory defined on the 7-dim boundary of a 8D bulk. To finalize,
it is shown how the E_{8} 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)

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### Submission history

[v1] 25 Aug 2009

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