Standard Model statistics of a Type II orientifold

TL;DR

The paper addresses the statistical properties of four-dimensional, N=1 supersymmetric intersecting D-brane vacua in a T^6/(Z2×Z2) orientifold, focusing on how often Standard Model-like gauge sectors arise and how observables correlate. A three-step computational algorithm is developed to construct solutions to tadpole, SUSY, and K-theory constraints, producing a large ensemble of vacua (~$1.6\times10^8$). Key findings include a strong suppression of three-generation SM-like configurations (about $10^{-9}$ of the ensemble), hidden-sector observables largely decoupled from the visible sector, and nontrivial correlations among rank, chirality, and couplings. The results provide quantitative landscape insight for Type II orientifolds and offer benchmarks for Gepner-model comparisons, motivating extensions to fluxes, heterotic duals, and GUT-like visible sectors.

Abstract

We analyse four-dimensional, supersymmetric intersecting D-brane models in a toroidal orientifold background from a statistical perspective. The distribution and correlation of observables, like gauge groups and couplings, are discussed. We focus on models with a Standard Model-like gauge sector, derive frequency distributions for their occurence and analyse the properties of the hidden sector.

Figures (7)

• Figure 1: Number of solutions found depending on the absolute value of the complex structure variables $U_I$.
• Figure 2: Frequency distributions of total rank and $U(M)$ gauge groups of all models.
• Figure 3: Number of quark and lepton generations with (red bars on the left) and without (blue bars on the right) enforcing a massless $U(1)$ .
• Figure 4: Frequency distributions of total rank and $U(M)$ gauge groups in the hidden sector of MSSM-models (red bars on the left) and MSSM models with massive $U(1)$ (blue bars on the right).
• Figure 5: Frequency distribution of $\alpha_s/\alpha_w$ in Standard Model-like configurations.