The landscape of intersecting brane models

TL;DR

This paper develops tools to analyze the space of intersecting brane models on a specific orientifold, proving finiteness, estimating model counts, analyzing intersection distributions, and constructing new models, with implications for string phenomenology.

Contribution

It introduces new analytical tools for intersecting brane models, proves finiteness on a specific orientifold, and constructs explicit 3-generation models.

Findings

Finite number of models satisfying supersymmetry equations.

Estimated models with specific gauge groups and three generations.

Intersection numbers are roughly independent and peaked around zero.

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.