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Clifford algebraic unification of conformal gravity with an extended standard model. (English) Zbl 1367.81158

Summary: A Clifford \(\mathrm{Cl}(5,\mathbb C)\) unified gauge field theory formulation of conformal gravity and \(U(4)\times U(4)\times U(4)\) Yang-Mills in \(4D\) is elaborated further. It is shown how the \(\mathrm{Cl}(5,\mathbb C)\) group has for physically relevant subgroup the one given by \(\mathrm{SU}(2,2)\times\mathrm{SU}(4)_C\times\mathrm{SU}(4)_L\times\mathrm{SU}(4)_R\), and which is compatible with the Coleman-Mandula theorem (in the absence of a mass gap). The proposals presented here for a Clifford algebraic unification of conformal gravity with an extended standard model deal mainly with models of four generations of fermions. Mirror fermions can be incorporated as well. Whether these mirror fermions are dark matter candidates is an open question. There are also residual \(U(1)\) groups within this Clifford group unification scheme that should play an important role in cosmology in connection to dark matter particles coupled to gravity via a bimetric extension of general relativity. Other four generation scenarios based on \(\mathrm{Cl}(6, \mathbb R)\), \(\mathrm{Cl}(8,\mathbb R)\) algebras, supersymmetric field theories and quaternions are discussed.

MSC:

81V22 Unified quantum theories
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81V17 Gravitational interaction in quantum theory
22E70 Applications of Lie groups to the sciences; explicit representations
11E88 Quadratic spaces; Clifford algebras
11G42 Arithmetic mirror symmetry
15A66 Clifford algebras, spinors
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