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

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.

arXiv comment21 pages, 9 figures, v3:published version

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• Graph Laplacians, Riemannian Manifolds and their Machine-Learning
• On the Search for Low $W_0$
• Coupling Selection Rules in Heterotic Calabi-Yau Compactifications
• Generalized Vanishing Theorems for Yukawa Couplings in Heterotic Compactifications
• Eigenvalues and eigenforms on Calabi-Yau threefolds
• Heterotic Line Bundle Models on Generalized Complete Intersection Calabi Yau Manifolds
• Universes as Big Data
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