Millions of Standard Models on Z6-prime?

TL;DR

This paper statistically analyzes supersymmetric standard-model-like spectra produced by intersecting D6-branes on the orientifold $T^6/\\mathbb{Z}_6'$. A statistical approach combines three-cycle intersection numbers and Chan-Paton matrices to obtain the complete massless spectrum, then computes tree-level gauge couplings and one-loop running. The study uncovers strong correlations between the number of chiral exotics, the number of (chiral) Higgs multiplets, and the values of gauge couplings, and identifies many SM-like realizations with a massless $U(1)_{B-L}$. It presents explicit three-generation models, both with and without hidden sectors, and demonstrates that the hidden sector is tightly constrained (rank $\leq 3$) and that the ensemble exhibits robust patterns across different background geometries. The results highlight significant structure in the string landscape and motivate further exploration of Yukawa couplings, threshold corrections, and alternative orbifold backgrounds.

Abstract

Using previous results on the statistics of intersecting D6-brane models on T^6/Z_6' we analyse solutions that resemble the gauge group and matter content of the supersymmetric standard model. In particular the structure of the hidden sector, the gauge coupling constants and chiral exotic matter content are computed and classified for all possible standard model-like configurations on this background. It turns out that the number of chiral exotics, Higgses and values of gauge couplings are strongly correlated. Some examples with the chiral spectrum of the supersymmetric standard model plus vector-like states and a massless U(1) B-L are discussed in detail.

Figures (9)

• Figure 1: Distribution of supersymmetric solutions to the RR tadpole equations with gauge group and chiral matter content of the standard model for different numbers of generations and the four geometries where such models occur (the other four possibilities AAa/b and BAa/b do not lead to any standard model--like solutions). The hidden sectors and number of chiral exotics have not been constrained. Note that this plot includes all possibilities, more than three generations do not occur.
• Figure 2: Distribution of the complex structure parameters $\varrho$ for the ABa geometry depending on the number of generations: yellow, red and blue correspond to three, two and one generation, respectively.
• Figure 3: The tree level ratio of fine structure constants $\alpha_s/\alpha_w$ for standard-like models on the ABa lattice (yellow, red and blue correspond to three, two and one generation,respectively).
• Figure 4: Combined distribution of the tree level ratios of $\alpha_s/\alpha_w$ and the weak mixing angle $\theta_w$ on the ABa lattice. A triangle, circle and square correspond to three, two and one generation models, respectively. Note that the colour scale on the right, which encodes the number of models with given values of $(\alpha_s/\alpha_w,{\rm sin}^2 \theta_w)$, is logarithmic.
• Figure 5: Number of "chiral" Higgs generation candidates (plus vector like lepton pairs in the presence of a $B-L$ symmetry) as defined in equation \ref{['eq:chh']} for three-generation standard model--like configurations on ABa.