The landscape of intersecting brane models

TL;DR

This work develops a systematic framework to analyze intersecting brane models on a T^6/(Z2 × Z2) orientifold, proving finiteness of SUSY configurations with fixed gauge data and deriving polynomial-scale bounds and enumeration algorithms. It analyzes the distribution of intersection numbers, showing near-independence across brane sectors and providing quantitative expectations for the number of Standard-Model-like vacua and new Pati-Salam constructions. The approach yields concrete counts and explicit model-building examples, and lays out a path to generalize to broader Calabi-Yau orientifolds while connecting IBM statistics to stabilized-vacua counting. Together, these results offer a tractable, quantitative map of a substantial string-vacua landscape sector and practical tools for constructing semi-realistic models.

Abstract

We develop tools for analyzing the space of intersecting brane models. We apply these tools to a particular T^6/Z_2^2 orientifold which has been used for model building. We prove that there are a finite number of intersecting brane models on this orientifold which satisfy the Diophantine equations coming from supersymmetry. We give estimates for numbers of models with specific gauge groups, which we confirm numerically. We analyze the distributions and correlations of intersection numbers which characterize the numbers of generations of chiral fermions, and show that intersection numbers are roughly independent, with a characteristic distribution which is peaked around 0 and in which integers with fewer divisors are mildly suppressed. As an application, the number of models containing a gauge group SU(3) x SU(2) x U(1) or SU(4) x SU(2) x SU(2) and 3 generations of appropriate types of chiral matter is estimated to be order O (10), in accord with previous explicit constructions. As another application of the methods developed in the paper, we construct a new pair of 3-generation SU(4) x SU(2) x SU(2) Pati-Salam models using intersecting branes. We conclude with a description of how this analysis can be generalized to a broader class of Calabi-Yau orientifolds, and a discussion of how the numbers of IBM's are related to numbers of stabilized vacua.