Towards Geometric D6-Brane Model Building on non-Factorisable Toroidal ${\mathbb{Z}}_4$-Orbifolds

Abstract

We present a geometric approach to D-brane model building on the non-factorisable torus backgrounds of $T^6/{\mathbb{Z}}_4$, which are $A_3\times A_3$ and $A_3\times A_1\times B_2$. Based on the counting of `short' supersymmetric three-cycles per complex structure {\it vev}, the number of physically inequivalent lattice orientations with respect to the anti-holomorphic involution $\mathcal{R}$ of the Type IIA/$\Omega \mathcal{R}$ orientifold can be reduced to three for the $A_3\times A_3$ lattice and four for the $A_3\times A_1\times B_2$ lattice. While four independent three-cycles on $A_3\times A_3$ cannot accommodate phenomenologically interesting global models with a chiral spectrum, the eight-dimensional space of three-cycles on $A_3\times A_1\times B_2$ is rich enough to provide for particle physics models, with several globally consistent two- and four-generation Pati-Salam models presented here. We further show that for fractional {\it sLag} three-cycles, the compact geometry can be rewritten in a $(T^2{)}^3$ factorised form, paving the way for a generalisation of known CFT methods to determine the vector-like spectrum and to derive the low-energy effective action for open string states.

Comments: 50+Appendix, 10 figures; v2: references added