Counting String Theory Standard Models

TL;DR

This paper estimates the number of heterotic string theory models that match the standard model's matter content, finding an exponential growth with the internal manifold's topological parameters, and predicts an enormous landscape of possible models.

Contribution

It derives an approximate analytic relation linking the count of consistent heterotic Calabi-Yau compactifications to topological data, validated for specific classes of manifolds.

Findings

Approximately 10^23 models for CICYs with up to 7 Kahler parameters.

Around 10^723 models for Calabi-Yau hypersurfaces in toric varieties.

Exponential scaling of models with Kahler parameters.

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.