134 Billion Intersecting Brane Models

TL;DR

This paper provides an exact count of 134 billion distinct intersecting brane vacua in type IIA string theory on a specific orientifold, offering insights into the string landscape's structure and diversity.

Contribution

It introduces a recursive, dynamic programming approach to efficiently count gauge-inequivalent brane configurations satisfying key consistency conditions.

Findings

Counted 134 billion distinct vacua.

Analyzed distributions of gauge group rank and moduli.

Developed methods applicable to other landscape regions.

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.