Supersymmetric Pati-Salam Models from Intersecting D6-branes: A Road to the Standard Model

TL;DR

This work develops a systematic construction of three-family $N=1$ supersymmetric Pati-Salam models from Type IIA orientifolds on $T^6/(oldsymbol{Z}_2\times\boldsymbol{Z}_2)$ with intersecting D6-branes, where the $SU(4)_C\times SU(2)_L\times SU(2)_R$ gauge factors arise from $U(n)$ branes and a confining $USp$ hidden sector. The authors derive the RR tadpole and SUSY conditions, analyze T-duality variations to classify inequivalent configurations, and implement a brane-splitting Higgs mechanism to reduce to the Standard Model via an $N=2$ subsector. A systematic search shows no viable solutions for two or three tilted tori, but identifies 11 inequivalent one-tilted models, eight with $\leq 8$ SM Higgs doublets and two achieving gauge coupling unification at the string scale; all models contain exotic matter. They discuss moduli stabilization and possible SUSY breaking via race-track gaugino condensation in the hidden sector, as well as phenomenological implications and avenues for future work in Yukawa textures, RG analyses, and composite states from strong hidden sectors.

Abstract

We provide a systematic construction of three-family N=1 supersymmetric Pati-Salam models from Type IIA orientifolds on $\IT^6/(\IZ_2\times \IZ_2)$ with intersecting D6-branes. All the gauge symmetry factors $SU(4)_C\times SU(2)_L \times SU(2)_R$ arise from the stacks of D6-branes with U(n) gauge symmetries, while the ``hidden sector'' is specified by $USp(n)$ branes, parallel with the orientifold planes or their ${\bf Z_2}$ images. The Pati-Salam gauge symmetry can be broken down to the $SU(3)_C\times SU(2)_L\times U(1)_{B-L} \times U(1)_{I_{3R}}$ via D6-brane splittings, and further down to the Standard Model via D- and F-flatness preserving Higgs mechanism from massless open string states in a N=2 subsector. The models also possess at least two confining hidden gauge sectors, where gaugino condensation can in turn trigger supersymmetry breaking and (some) moduli stabilization. The systematic search yields 11 inequivalent models: 8 models with less than 9 Standard model Higgs doublet-pairs and 1 model with only 2 Standard Model Higgs doublet-pairs, 2 models possess at the string scale the gauge coupling unification of $SU(2)_L$ and $SU(2)_R$, and all the models possess additional exotic matters. We also make preliminary comments on phenomenological implications of these models.