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AN EXCEPTIONAL E₈ GAUGE THEORY OF GRAVITY IN D = 8, CLIFFORD SPACES AND GRAND UNIFICATION

CARLOS CASTRO

Center for Theoretical Studies of Physical Systems, Clark Atlanta University, Atlanta, GA 30314, USA

https://doi.org/10.1142/S0219887809003916Cited by:7 (Source: Crossref)

Abstract

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 quarticE₈ 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.

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