Counting String Theory Standard Models

Abstract

We derive an approximate analytic relation between the number of consistent heterotic Calabi-Yau compactifications of string theory with the exact charged matter content of the standard model of particle physics and the topological data of the internal manifold: the former scaling exponentially with the number of Kahler parameters. This is done by an estimate of the number of solutions to a set of Diophantine equations representing constraints satisfied by any consistent heterotic string vacuum with three chiral massless families, and has been computationally checked to hold for complete intersection Calabi-Yau threefolds (CICYs) with up to seven Kahler parameters. When extrapolated to the entire CICY list, the relation gives about 10^23 string theory standard models; for the class of Calabi-Yau hypersurfaces in toric varieties, it gives about 10^723 standard models.

6 pages, 4 figures, comments and refs added

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• Explore and Exploit with Heterotic Line Bundle Models
• Evolving Heterotic Gauge Backgrounds: Genetic Algorithms versus Reinforcement Learning
• Heterotic String Model Building with Monad Bundles and Reinforcement Learning
• Calabi-Yau Metrics, Energy Functionals and Machine-Learning
• General F-theory models with tuned $(\mathrm{SU}(3)\times \mathrm{SU}(2)\times U(1))/{\mathbb{Z}}_6$ symmetry
• Jumping Spectra and Vanishing Couplings in Heterotic Line Bundle Standard Models
• Generalized Vanishing Theorems for Yukawa Couplings in Heterotic Compactifications
• Tadpole conjecture in non-geometric backgrounds
• Generic construction of the Standard Model gauge group and matter representations in F-theory
• Heterotic Line Bundle Models on Generalized Complete Intersection Calabi Yau Manifolds
• Dark photon portal into mirror world
• Universes as Big Data
• Topological Data Analysis for the String Landscape
• cymyc -- Calabi-Yau Metrics, Yukawas, and Curvature
• Yukawa Textures From Singular Spectral Data
• Beyond Algebraic Superstring Compactification