Revisiting the supersymmetric Pati–Salam models from intersecting D6-branes

Employing novel random and supervised scanning methods, we systematically revisit the construction of three-family N=1 supersymmetric Pati–Salam models in Type IIA orientifolds on T${}^6$/($Z_2$ × $Z_2$) with intersecting D6-branes. Arising from the stacks of D6-branes with U(n) gauge symmetries, the Pati–Salam gauge symmetries SU(4)${}_C$ × SU(2)${}_L$ × SU(2)${}_R$ can be broken down to the Standard Model via D-brane splitting as well as D- and F-flatness preserving Higgs mechanism. Also, the hidden sector contains USp(n) branes, which are parallel with the orientifold planes or their $Z_2$ images. We find that the Type II T-duality in the previous study is not an equivalent relation in Pati–Salam model building if the model is not invariant under SU(2)${}_L$ and SU(2)${}_R$ exchange, and provides a way to obtain new models. We systematically construct the new models with three families, which usually do not have gauge coupling unification at the string scale. We for the first time construct the Pati–Salam models with at least one wrapping number whose absolute value reaching 5. In particular, for one large wrapping number equal to 5, we find that one kind of model carries more refined gauge couplings, and thus with more possibilities to have approximate gauge coupling unification.