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A CHERN–SIMONS E₈ GAUGE THEORY OF GRAVITY IN D = 15, GRAND UNIFICATION AND GENERALIZED GRAVITY IN CLIFFORD SPACES

CARLOS CASTRO

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

https://doi.org/10.1142/S0219887807002545Cited by:14 (Source: Crossref)

Abstract

A novel Chern–Simons E₈ gauge theory of gravity in D = 15 based on an octicE₈ invariant expression in D = 16 (recently constructed by Cederwall and Palmkvist) is 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) of this Chern–Simons E₈ gauge theory. We review the construction showing why the ordinary 11D Chern–Simons gravity theory (based on the Anti de Sitter group) can be embedded into a Clifford-algebra valued gauge theory and that an E₈ Yang–Mills field theory is a small sector of a Clifford (16) algebra gauge theory. An E₈ gauge bundle formulation was instrumental in understanding the topological part of the 11-dim M-theory partition function. The nature of this 11-dim E₈ gauge theory remains unknown. We hope that the Chern–Simons E₈ gauge theory of gravity in D = 15 advanced in this work may shed some light into solving this problem after a dimensional reduction.

Keywords:

References

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