The complete search for the supersymmetric Pati-Salam models from intersecting D6-branes

We construct a systematic method to build all the possible three-family N = 1 supersymmetric Pati-Salam models from Type IIA orientifolds on T-6/(Z(2) x Z(2)) with intersecting D6-branes, in which the SU(4)(C) x SU(2)(L) x SU(2)(R) gauge symmetry can be broken down to the SU(3)(C) x SU(2)(L) x U(1)(Y) Standard Model gauge symmetry by the D-brane splitting and supersymmetry preserving Higgs mechanism. This is essentially achieved by solving all the common solutions for three generation conditions, RR tadpole cancellation conditions, and N = 1 supersymmetry conditions with deterministic algorithm. We find that there are 202752 possible supersymmetric Pati-Salam models in total, and show that there are only 33 independent models with different gauge coupling relations at GUTs scale after modding out equivalent relations, such as T-dualities, etc. In particular, there is one and only one independent model which has gauge coupling unification. Furthermore, one can construct other types of intersecting D-brane models utilizing such deterministic algorithm, and therefore we suggest a brand new method for D-brane model building.