Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2003-09-17
JHEP 0403 (2004) 040
Physics
High Energy Physics
High Energy Physics - Phenomenology
Latex, 33 pages, minor changes
Scientific paper
10.1088/1126-6708/2004/03/040
After we study the 6-dimensional ${\cal N} = (1, 1)$ supersymmetry breaking and $R$ symmetry breaking on $M^4\times T^2/Z_n$, we construct two ${\cal N} = (1, 1)$ supersymmetric $E_6$ models on $M^4\times T^2/Z_3$ where $E_6$ is broken down to $SO(10)\times U(1)_X$ by orbifold projection. In Model I, three families of the Standard Model fermions arise from the zero modes of bulk vector multiplet, and the $R$ symmetry $U(1)_F^{I} \times SU(2)_{{\bf 4}_-}$ can be considered as flavour symmetry. This may explain why there are three families of fermions in the nature. In Model II, the first two families come from the zero modes of bulk vector multiplet, and the flavour symmetry is similar. In these models, the anomalies can be cancelled, and we have very good fits to the SM fermion masses and mixings. We also comment on the ${\cal N}=(1, 1)$ supersymmetric $E_6$ models on $M^4\times T^2/Z_4$ and $M^4\times T^2/Z_6$, SU(9) models on $M^4\times T^2/Z_3$, and SU(8) models on $T^2$ orbifolds.
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