Deep learning and k-means clustering in heterotic string vacua with line bundles

Hajime Otsuka,Kenta Takemoto

doi:10.1007/jhep05(2020)047

Abstract

We apply deep-learning techniques to the string landscape, in particular, SO(32) heterotic string theory on simply-connected Calabi-Yau threefolds with line bundles. It turns out that three-generation models cluster in particular islands specified by deep autoencoder networks and k-means++ clustering. Especially, we explore mutual relations between model parameters and the cluster with densest three-generation models (called “3-generation island”). We find that the 3-generation island has a strong correlation with the topological data of Calabi-Yau threefolds, in particular, second Chern class of the tangent bundle of the Calabi-Yau threefolds. Our results also predict a large number of Higgs pairs in the 3-generation island.

Highlights

(4D) string models based on the direct flux breaking scenario
After performing the autoencoder and the k-means++ clustering to the vacua, we find that three-generation models are clustered in particular islands, in a similar to the analysis in the toroidal orbifold models [6] and we call the cluster with densest three-generation models “3-generation island”
The cluster located around (0.54,0.47) in figure 3 has the highest ratio (∼= 19.15%) among total 26 clusters and this cluster is identified with the 3-generation island

Summary

Introduction

(4D) string models based on the direct flux breaking scenario It opens up a new possibility of searching for the three-generation SM. The direct flux breaking scenario in SO(32) heterotic string theory is motivated by its S- and T-dual intersecting D6-brane models in Type IIA string theory, where several stacks of D-branes directly lead to the MSSM-like gauge group. The purpose of this paper is to reveal the nature of SM vacua in SO(32) heterotic line bundle models by employing the neural network technique, in particular the origin of three generations of quarks and leptons. Before applying the deep autoencoder to the dataset of heterotic line bundle models, we briefly review the heterotic line bundle models developed in refs. [15, 16, 19, 26,27,28,29] with an emphasis on the phenomenological and theoretical constraints

Objectives

Methods

Results

Conclusion