Quantum Gravity and String Theory


A Clifford Cl(5,C) Unified Gauge Field Theory of Conformal Gravity, Maxwell and U(4) x U(4) Yang-Mills in 4D

Authors: Carlos Castro

A Clifford Cl(5,C) Unified Gauge Field Theory of Conformal Gravity, Maxwell and U(4)xU(4) Yang-Mills in 4D is rigorously presented extending our results in prior work. The Cl(5,C) = Cl(4,C)⊕Cl(4,C) algebraic structure of the Conformal Gravity, Maxwell and U(4)xU(4) Yang-Mills unification program advanced in this work is that the group structure given by the direct products U(2, 2)xU(4)xU(4) = [SU(2, 2)]spacetimex [U(1) x U(4) x U(4)]internal is ultimately tied down to four-dimensions and does not violate the Coleman-Mandula theorem because the spacetime symmetries (conformal group SU(2, 2) in the absence of a mass gap, Poincare group when there is mass gap) do not mix with the internal symmetries. Similar considerations apply to the supersymmetric case when the symmetry group structure is given by the direct product of the superconformal group (in the absence of a mass gap) with an internal symmetry group so that the Haag-Lopuszanski-Sohnius theorem is not violated. A generalization of the de Sitter and Anti de Sitter gravitational theories based on the gauging of the Cl(4, 1,R),Cl(3, 2,R) algebras follows. We conclude with a few remarks about the complex extensions of the Metric Affine theories of Gravity (MAG) based on GL(4,C) xs C4, the realizations of twistors and the N = 1 superconformal su(2, 2|1) algebra purely in terms of Clifford algebras and their plausible role in Witten's formulation of perturbative N = 4 super Yang-Mills theory in terms of twistor-string variables.

Comments: 22 pages, submitted to Advances in Applied Clifford Algebras (AACA).

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Submission history

[v1] 12 Jan 2011

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