A grand unification preon model with E6 metacolor |
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| Affiliation: | 1. Gafsa University, Preparatory Institute for Engineering Studies of Gafsa, Tunisia;2. Taibah University, Faculty of Sciences, Madina, Saudi Arabia;3. Western Kentucky University, Bowling Green, KY 42101, USA;4. Faculty of Sciences of Tunis, Department of Mathematics, 2092 Campus Universitaire El Manar, Tunisia;1. Intelligent Manufacturing Systems (IMS) Center, Department of Industrial and Manufacturing Systems Engineering, University of Windsor, Windsor, ON, Canada;2. Mechanical and Industrial Engineering, University of Minnesota Duluth, Duluth, MN, USA;1. Departamento de Matemática Aplicada, Ciencia e Ingeniería de los Materiales y Tecnología Electrónica, ESCET Universidad Rey Juan Carlos, 28933 Móstoles (Madrid), Spain;2. Departamento de Matemática Aplicada y Estadística, Facultad de Ciencias Económicas y Empresariales, Universidad San Pablo-CEU, CEU Universities, Calle Julián Romea 23, 28003 Madrid, Spain;3. Departamento de Álgebra, Geometría y Topología, Universidad Complutense de Madrid and Instituto de Matematica Interdisciplinar, Plaza de Ciencias 3, 28040 Madrid, Spain |
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| Abstract: | We have constructed a version of the chiral three-preon model E6 × SO(10) that satisfies the condition of asymptotic freedom in the metacolor and composite color-flavor sectors. The construction is based on the global color-flavor symmetry group SU(18). By applying the 't Hooft anomaly matching condition to the subgroup SU(16) × SU(2) of SU(18), together with a few physical constraints, we obtain a unique solution that gives rise to precisely three generations of the spinorial representation 16 of SO(10) without exotics. Except for N = 18, no solution exists for the global color-flavor group satisfying metacolor asymptotic freedom (N < 22) when SU(N) breaks to SU(16) × SU(N − 16). |
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