On generalized Yang-Mills theories and extensions of the standard model in Clifford (tensorial) spaces

2010

Int. J. Mod. Phys. A

Self Cite

It is shown how a Conformal Gravity and U (4)×U (4) Yang-Mills Grand Unification model in f our dimensions can be attained from a Clifford Gauge Field Theory in C-spaces (Clifford spaces) based on the (complex) Clifford Cl(4, C) algebra underlying a complexified four dimensional spacetime (8 real dimensions). Upon taking a real slice, and after symmetry breaking, it leads to ordinary Gravity and the Standard Model in four real dimensions. A brief conclusion about the Noncommutative star product deformations of this Grand Unified Theory of Gravity with the other forces of Nature is presented.

Section: Conformal Gravity and U (4)×u (4) Yang-millsmentioning

confidence: 99%

“…Tensorial Generalized Yang-Mills in C-spaces (Clifford spaces) based on poly-vector valued (anti-symmetric tensor fields) gauge fields A M (X) and field strengths F M N (X) have ben studied in [19], [25] where X = X M Γ M is a C-space poly-vector valued coordinate…”

Section: Conformal Gravity and U (4)×u (4) Yang-millsmentioning

confidence: 99%

THE CLIFFORD SPACE GEOMETRY OF CONFORMAL GRAVITY AND U(4) × U(4) YANG–MILLS UNIFICATION

2010

Int. J. Mod. Phys. A

Self Cite

“…A unified model involving an 8-dim space based on the Clifford algebra Cl(8) and octonions has been constructed by Smith [17]. A generalization of Smith's model to C-spaces was advanced in [49].…”

Section: Octonionic Geometry Of Noncommutative and Nonassociative Spamentioning

confidence: 99%

“…where G M N is the curved C-space ( Clifford space ) metric that can be decomposed into sums of antisymmetrized products of the ordinary D = 4 spacetime metric as (69c) A lot remains ahead, some preliminary work can be found in [47], [48], [49], [50] , [51] , [52], [53], [12].…”

Section: Octonionic Geometry Of Noncommutative and Nonassociative Spamentioning

confidence: 99%

On the noncommutative and nonassociative geometry of octonionic space time, modified dispersion relations and grand unification

Journal of Mathematical Physics

2007

Self Cite

The Octonionic Geometry (Gravity) developed long ago by Oliveira and Marques is extended to Noncommutative and Nonassociative Spacetime coordinates associated with octonionic-valued coordinates and momenta. The octonionic metric G µν already encompasses the ordinary spacetime metric g µν , in addition to the Maxwell U (1) and SU (2) Yang-Mills fields such that implements the Kaluza-Klein Grand Unification program without introducing extra spacetime dimensions. The color group SU (3) is a subgroup of the exceptional G 2 group which is the automorphism group of the octonion algebra. It is shown that the flux of the SU (2) Yang-Mills field strength F µν through the areamomentum Σ µν in the internal isospin space yields corrections O(1/M 2 P lanck ) to the energy-momentum dispersion relations without violating Lorentz invariance as it occurs with Hopf algebraic deformations of the Poincare algebra. The known Octonionic realizations of the Clifford Cl(8), Cl(4) algebras should permit the construction of octonionic string actions that should have a correspondence with ordinary string actions for strings moving in a curved Clifford-space target background associated with a Cl(3, 1) algebra.

“…. of higher rank (higher spin theories) [13]. The most general action onto which the action (3.9), (3.10) itself can be embedded requires a tensorial gauge field theory [13] (generalized Yang-Mills theories) and an integration with respect to all the Clifford-valued coordinates X = X M Γ M corresponding to the 2 D -dim C-space associated with the underlying Cl(2n)-algebra in D = 2n dimensions…”

Section: On Chern-simons-clifford Gravitymentioning

confidence: 99%

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

Int. J. Geom. Methods Mod. Phys.

2007

Self Cite

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 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 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 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 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 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 reduction.