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Counting string theory standard models

Constantin, A., He, Y. ORCID: 0000-0002-0787-8380 and Lukas, A. (2019). Counting string theory standard models. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 792, pp. 258-262. doi: 10.1016/j.physletb.2019.03.048

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 Kähler 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 Kähler parameters. When extrapolated to the entire CICY list, the relation gives ∼10 23 string theory standard models; for the class of Calabi-Yau hypersurfaces in toric varieties, it gives ∼10 723 standard models.

Publication Type: Article
Additional Information: ©2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Subjects: Q Science > QA Mathematics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
URI: http://openaccess.city.ac.uk/id/eprint/22130
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