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.

Automated summary

We present a systematic method for constructing all possible three-family N=1 supersymmetric Pati-Salam models using intersecting D6-branes in Type IIA orientifolds on T-6/(Z(2) x Z(2)). By using a deterministic algorithm, we solve the conditions for three generation conditions, RR tadpole cancellation conditions, and N=1 supersymmetry conditions. We find a total of 202752 possible supersymmetric Pati-Salam models, but only 33 independent models with different gauge coupling relations at the grand unification theory (GUT) scale. One of these models exhibits gauge coupling unification. This method also provides a new approach for constructing intersecting D-brane models.