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.

50+Appendix, 10 figures; v2: references added

References in corpus (21)

• Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes
• A Mini-Landscape of Exact MSSM Spectra in Heterotic Orbifolds
• Orientifolds, hypercharge embeddings and the Standard Model
• Lectures on Generalized Complex Geometry for Physicists
• Millions of Standard Models on Z6-prime?
• Instantons and Holomorphic Couplings in Intersecting D-brane Models
• Toroidal Orientifolds in IIA with General NS-NS Fluxes
• Thresholds for Intersecting D-branes Revisited
• D6-branes and torsion
• Geography of Fields in Extra Dimensions: String Theory Lessons for Particle Physics
• Towards a Realistic Type IIA T^6/Z_4 Orientifold Model with Background Fluxes, Part 1: Moduli Stabilization
• The Importance of Being Rigid: D6-Brane Model Building on T6/Z2xZ6' with Discrete Torsion
• Gauge Thresholds and Kaehler Metrics for Rigid Intersecting D-brane Models
• Type IIA Pati-Salam Flux Vacua
• Statistics of intersecting D-brane models on T^6/Z_6
• Constructing the supersymmetric Standard Model from intersecting D6-branes on the Z_6' orientifold
• Oddness from Rigidness
• Model building with intersecting D6-branes on smooth Calabi-Yau manifolds
• Rigour and Rigidity: Systematics on particle physics D6-brane models on Z(2)xZ(6)
• Type IIA orientifolds and orbifolds on non-factorizable tori
• Circling the Square: Deforming fractional D-branes in Type II/$\Omega \mathcal{R}$ orientifolds

Cited by in corpus (1)

• From Type II string theory towards BSM/dark sector physics