134 Billion Intersecting Brane Models

Abstract

The landscape of string vacua is very large, but generally expected to be finite in size. Enumerating the number and properties of the vacua is an important task for both the landscape and the swampland, in part to gain a deeper understanding of what is possible and "generic". We obtain an exact counting of distinct intersecting brane vacua of type IIA string theory on the ${\mathbb{T}}^6/{\mathbb{Z}}_2\times {\mathbb{Z}}_2$ orientifold. Care is taken to only count gauge-inequivalent brane configurations. Leveraging the recursive nature by which branes may be added together one-by-one, we use dynamic programming to efficiently count the number of solutions of the tadpole, K-theory and supersymmetry consistency conditions. The distributions of 4D gauge group rank and complex structure moduli for the entire ensemble of intersecting brane vacua are presented. The methods we developed here may be useful in obtaining sharp upper and lower bounds on other corners of the landscape.

arXiv comment13 pages + 7 pages of appendices, 5 figures, 134 billion vacua; v2: incomplete gauge-fixing in section 3 amended and all following tables/figures updated, minor corrections, accepted to JHEP

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• Towards a complete classification of 6D supergravities
• String-scale Gauge Coupling Relations in the Supersymmetric Pati-Salam Models from Intersecting D6-branes
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
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• Three-family supersymmetric Pati-Salam models from intersecting D6-branes on rigid cycles