N=1 supersymmetric SU(12)C x SU(2)L x SU(2)R models, SU(4)C x SU(6)L x SU(2)R models, and SU(4)C x SU(2)L x SU(6)R models from intersecting D6-branes

For the first time we systematically discuss the N = 1 supersymmetric SU(12)(C) x SU(2)(L) x SU(2)(R) models, SU(4)(C) x SU(6)(L) x SU(2)(R )models, and SU(4)(C) x SU(2)(L) x SU(6)(R) models from the type IIA orientifolds on T-6 / (Z(2) x Z(2)) with intersecting D6-branes. These gauge symmetries can be broken down to the Pati-Salam gauge symmetry SU(4)(C) x SU(2)(L) x SU(2)(R) via three SU(12)(C)/SU(6)(L)/SU(6)(R) adjoint representation Higgs fields, and further down to the Standard Model (SM) via the D-brane splitting and Higgs mechanism. We obtain three families of the SM fermions, and have the left-handed three-family SM fermion unification in the SU(4)(C) x SU(6)(L) x SU(2)(R) models, and the right-handed three-family SM fermion unification in the SU(4)(C) x SU(2)(L) x SU(6)(R) models. Utilizing mathematical analysis, we exclude the generalized SU(12)(C) x SU(2)(L) x SU(2)(R) models by requiring the conditions for constructing Minimal Supersymmetric Standard Model models. Moreover, the SU(4)(C) x SU(6)(L) x SU(2)(R) models and SU(4)(C) x SU(2)(L) x SU(6)(R) models are related by the left and right gauge symmetry exchanging, as well as a variation of type II T-duality. The hidden sector contains USp(n) branes, which are parallel with the orientifold planes or their Z(2) images and might break the supersymmetry via gaugino condensations.

Automated summary

For the first time, N = 1 supersymmetric SU(12)(C) x SU(2)(L) x SU(2)(R) models, SU(4)(C) x SU(6)(L) x SU(2)(R) models, and SU(4)(C) x SU(2)(L) x SU(6)(R) models were systematically discussed in the context of type IIA orientifolds on T-6 / (Z(2) x Z(2)) with intersecting D6-branes. By using mathematical analysis, some models were excluded and the relationship between the SU(4)(C) x SU(6)(L) x SU(2)(R) models and SU(4)(C) x SU(2)(L) x SU(6)(R) models, related by left and right gauge symmetry exchanging, as well as a variation of type II T-duality, was explored.