Chiral supersymmetric models on an orientifold of Z_4 x Z_2 with intersecting D6-branes

TL;DR

The paper develops chiral, supersymmetric vacua from intersecting D6-branes on the Type IIA orientifold $T^6/({\mathbb Z}_4 \times {\mathbb Z}_2)$, deriving RR tadpole cancellation and a disc-level NSNS scalar potential while detailing the general open-string spectrum. It then constructs two explicit chiral models with a Pati-Salam gauge group: a four-generation model and a three-generation model that, after brane recombination, yields the SM-like spectrum with right-handed neutrinos. The results demonstrate that realistic-like chiral SUSY vacua can arise in this orientifold, providing concrete frameworks for further phenomenological analysis of Yukawas, gauge thresholds, and symmetry breaking. The work motivates broader explorations of moduli stabilization and dual descriptions within this class of intersecting-brane constructions.

Abstract

We investigate intersecting D6-branes on an orientifold of type IIA theory in the orbifold background T^6/(Z_4 x Z_2) with the emphasis on finding chiral spectra. RR tadpole cancellation conditions and the scalar potential at disc level are computed. The general chiral spectrum is displayed, and two supersymmetric models with a Pati-Salam group are shown,one with four generations and the other one with three generations and exactly the chiral matter content of the SM plus right handed neutrinos.

Figures (5)

• Figure 1: The possible choices of the compactification lattices per two-torus. ${\mathbb Z}_4$ fixed points are depicted by filled circles, the additional points invariant under ${\mathbb Z}_2$ subsymmetries by empty circles. The basis of each two-torus in our convention is displayed in blue. The two possible choices of the third lattice correspond to a vanishing and non-trivial antisymmetric tensor background on $\Tilde{T}^2_3$ in the T-dual type IIB orientifold, respectively.
• Figure 2: The four orbits of O6-planes. Each orbit consists of an O6-plane and its image under the ${\mathbb Z}_4$ generator $\Theta$. The black and the purple cycles belong to one orbit, the red and the yellow cycles form another orbit. The remaining orbits consist of the blue and cyan cycles and the green and brown ones.
• Figure 3: Orbit of a D6-brane with wrapping numbers $(n^a_1,m^a_1)=(2,1)$, $(n^a_2,m^a_2)=(1,2)$, $(n^a_3,m^a_3)=(1,2)$ on a tilted torus $T^2_3$, i.e. $b=1/2$. The brane $a$ and its ${\mathbb Z}_4$ image $(\Theta a)$ are represented by solid red lines whereas the mirror images $a'$ and $(\Theta a)'$ are depicted by dashed red lines.
• Figure 4:
• Figure 5: Special supersymmetric D6-brane configurations. Only one representant of each orbit containing four distinct D6-branes is depicted for the sake of clarity. The lattice on $T^2_1 \times T^2_2$ is AB, $T^2_3$ can be rectangular or tilted.