The Complete Search for the Supersymmetric Pati-Salam Models from Intersecting D6-Branes

Abstract

We construct a systematic method to build all the possible three-family $\mathcal{N}=1$ supersymmetric Pati-Salam models from Type IIA orientifolds on ${\mathbb{T}}^6/({\mathbb{Z}}_2\times {\mathbb{Z}}_2)$ with intersecting D6-branes, in which the $SU(4{)}_C\times SU(2{)}_L\times SU(2{)}_R$ gauge symmetry can be broken down to the $SU(3{)}_C\times SU(2{)}_L\times U(1{)}_Y$ 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 the RR tadpole cancellation conditions, $\mathcal{N}=1$ supersymmetry conditions, and three generation 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 string 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.

Comments: references added. arXiv admin note: text overlap with arXiv:1910.04530, arXiv:1912.11633, arXiv:2112.09630