GENERALIZED GRAVITY IN CLIFFORD SPACES, VACUUM ENERGY AND GRAND UNIFICATION

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 cancelation 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 non-commutative 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.