C. Castro: Generalized Gravity in Clifford Spaces, Vacuum Energy and Grand Unification


by Carlos Castro
Center for Theoretical Studies of Physical Systems
Clark Atlanta University, Atlanta, GA. 30314; USA
perelmanc@hotmail.com
August, 2010
submitted to Int. J. Mod. Phys. A, 21 pages.

Abstract Polyvector-valued gauge field theories in Clifford spaces are used to construct a novel Cl(3, 2) gauge theory of gravity that furnishes modified curvature and torsion tensors leading to important modifications of the standard gravitational action with a cosmological constant. Vacuum solutions exist which allow a cancellation of the contributions of a very large cosmological constant term and the extra terms present in the modified field equations. Generalized gravitational actions in Clifford-spaces are provided and some of their physical implications are discussed. It is shown how the 16 fermions and their masses in each family can be accommodated within a Cl(4) gauge field theory. In particular, the Higgs fields admit a natural Clifford-space interpretation that differs from the one in the Chamseddine-Connes spectral action model of Noncommutative geometry. We finalize with a discussion on the relationship with the Pati-Salam color-flavor model group SU(4)_C ×SU(4)_F and its symmetry breaking patterns. An Appendix is included with useful Clifford algebraic relations.

Source: Email by C. Castro, Saturday, September 11, 2010, 8:17 AM, czarlosromanov_AT_yahoo.com

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