Chiral Four-Dimensional N=1 Supersymmetric Type IIA Orientifolds from Intersecting D6-Branes

TL;DR

We present four-dimensional $N=1$ supersymmetric Type IIA orientifolds on $T^6/(\,\mathbb{Z}_2\times\mathbb{Z}_2\,)$ with D6-branes at angles that generate chiral gauge sectors. Using explicit tadpole cancellation conditions and a SUSY-preserving angle constraint, we construct multiple models, including the first three-family Standard Model–like vacuum and a supersymmetric $SU(5)$ GUT, with detailed spectra and hypercharge embeddings. The work further analyzes small instanton transitions, D-term SUSY breaking via untwisted moduli, and the M-theory lift to $G_2$ holonomy, connecting brane recombination to geometric transitions and suggesting a geometrically rich path to realistic chiral vacua. Overall, it provides a concrete, geometrically controlled framework for realizing chiral 4D vacua in Type II string theory and highlights notable phenomenological and duality-driven insights for future exploration.

Abstract

We construct N=1 supersymmetric four-dimensional orientifolds of type IIA on T^6/(Z_2 x Z_2) with D6-branes intersecting at angles. The use of D6-branes not fully aligned with the O6-planes in the model allows for a construction of many supersymmetric models with chiral matter, including those with the Standard Model and grand unified gauge groups. We perform a search for realistic gauge sectors, and construct the first example of a supersymmetric type II orientifold with SU(3)_C x SU(2)_L x U(1)_Y gauge group and three quark-lepton families. In addition to the supersymmetric Standard Model content, the model contains right-handed neutrinos, a (chiral but anomaly-free) set of exotic multiplets, and diverse vector-like multiplets. The general class of these constructions are related to familiar type II orientifolds by small instanton transitions, which in some cases change the number of generations, as discussed in specific models. These constructions are supersymmetric only for special choices of untwisted moduli. We briefly discuss the supersymmetry breaking effects away from that point. The M-theory lift of this general class of supersymmetric orientifold models should correspond to purely geometrical backgrounds admitting a singular G_2 holonomy metric and leading to four-dimensional M-theory vacua with chiral fermions.

Figures (2)

• Figure 1: O6-planes in the orientifold of $\bf T^6/(\bf Z_2\times \bf Z_2)$.
• Figure 2: O6-planes in the orientifold of $\bf T^6/(\bf Z_2\times \bf Z_2)$ where the third two-tori is tilted.