The final model building for the supersymmetric Pati–Salam models from intersecting D6-branes

Abstract

Abstract All the possible three-family $${\mathcal N}=1$$ N = 1 supersymmetric Pati–Salam models constructed with intersecting D6-branes from Type IIA orientifolds on $$T^6/(\mathbb {Z}_2\times \mathbb {Z}_2)$$ T 6 / ( Z 2 × Z 2 ) are recently presented in arXiv:2112.09632 . Taking models with largest wrapping number 5 and approximate gauge coupling unification at GUT scale as examples, we show string scale gauge coupling unification can be realized through two-loop renormalization group equation running by introducing seven pairs of vector-like particles from $${\mathcal N}=2$$ N = 2 sector. The number of these introduced vector-like particles are fully determined by the brane intersection numbers while there are two D6-brane parallel to each other along one two-torus. We expect this will solve the gauge coupling unification problem in the generic intersecting brane worlds by introducing vector-like particles that naturally included in the $${\mathcal N}=2$$ N = 2 sector.