1st Reading October 26, 2007 18:56 WSPC/IJGMMP-J043 00254 International Journal of Geometric Methods in Modern Physics 1 Vol. 4, No. 8 (2007) 1–19 c  World Scientific Publishing Company 3 A CHERN–SIMONS E 8 GAUGE THEORY OF GRAVITY IN 5 D = 15, GRAND UNIFICATION AND GENERALIZED GRAVITY IN CLIFFORD SPACES 7 CARLOS CASTRO Center for Theoretical Studies of Physical Systems 9 Clark Atlanta University, Atlanta, GA 30314, USA castro@ctsps.cau.edu 11 Received 22 March 2007 Accepted 13 July 2007 13 A novel Chern–Simons E 8 gauge theory of gravity in D = 15 based on an octic E 8 invariant expression in D = 16 (recently constructed by Cederwall and Palmkvist) is 15 developed. A grand unification model of gravity with the other forces is very plausible within the framework of a supersymmetric extension (to incorporate spacetime fermions) 17 of this Chern–Simons E 8 gauge theory. We review the construction showing why the ordinary 11D Chern–Simons gravity theory (based on the Anti de Sitter group) can 19 be embedded into a Clifford-algebra valued gauge theory and that an E 8 Yang–Mills field theory is a small sector of a Clifford (16) algebra gauge theory. An E 8 gauge 21 bundle formulation was instrumental in understanding the topological part of the 11- dim M-theory partition function. The nature of this 11-dim E 8 gauge theory remains 23 unknown. We hope that the Chern–Simons E 8 gauge theory of gravity in D = 15 advanced in this work may shed some light into solving this problem after a dimensional 25 reduction. Keywords : 27 1. Introduction Exceptional, Jordan, Division and Clifford algebras are deeply related and essen- 29 tial tools in many aspects of Physics [3, 5, 8, 9, 14–20]. Ever since the discovery [1] that 11D supergravity, when dimensionally reduced to an n-dim torus led to 31 maximal supergravity theories with hidden exceptional symmetries E n for n ≤ 8, it has prompted intensive research to explain the higher dimensional origins of these 33 hidden exceptional E n symmetries [2, 6]. More recently, there has been a lot of interest in the infinite-dim hyperbolic Kac–Moody E 10 and nonlinearly realized 35 E 11 algebras arising in the asymptotic chaotic oscillatory solutions of supergravity fields close to cosmological singularities [1, 2]. 37 The classification of symmetric spaces associated with the scalars of N extended supergravity theories, emerging from compactifications of 11D supergravity to lower 39 dimensions, and the construction of the U -duality groups as spectrum-generating 1