Three fermion generations with two unbroken gauge symmetries from the complex sedenions

Autor: Adam B. Gillard, Niels G. Gresnigt
Jazyk: angličtina
Rok vydání: 2019
Předmět:
Zdroj: European Physical Journal C: Particles and Fields, Vol 79, Iss 5, Pp 1-11 (2019)
Druh dokumentu: article
ISSN: 1434-6044
1434-6052
DOI: 10.1140/epjc/s10052-019-6967-1
Popis: Abstract We show that three generations of leptons and quarks with unbroken Standard Model gauge symmetry $$SU(3)_c\times U(1)_{em}$$ SU(3)c×U(1)em can be described using the algebra of complexified sedenions $${\mathbb {C}}\otimes {\mathbb {S}}$$ C⊗S . A primitive idempotent is constructed by selecting a special direction, and the action of this projector on the basis of $${\mathbb {C}}\otimes {\mathbb {S}}$$ C⊗S can be used to uniquely split the algebra into three complex octonion subalgebras $${\mathbb {C}}\otimes {\mathbb {O}}$$ C⊗O . These subalgebras all share a common quaternionic subalgebra. The left adjoint actions of the 8 $${\mathbb {C}}$$ C -dimensional $${\mathbb {C}}\otimes {\mathbb {O}}$$ C⊗O subalgebras on themselves generates three copies of the Clifford algebra $${\mathbb {C}}\ell (6)$$ Cℓ(6) . It was previously shown that the minimal left ideals of $${\mathbb {C}}\ell (6)$$ Cℓ(6) describe a single generation of fermions with unbroken $$SU(3)_c\times U(1)_{em}$$ SU(3)c×U(1)em gauge symmetry. Extending this construction from $${\mathbb {C}}\otimes {\mathbb {O}}$$ C⊗O to $${\mathbb {C}}\otimes {\mathbb {S}}$$ C⊗S naturally leads to a description of exactly three generations.
Databáze: Directory of Open Access Journals
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