City Research Online

Abstract

In this thesis we explore various aspects of Calabi-Yau (CY) and G2 manifolds and string compactifications over them. We do so using techniques taken from the fields of data science and machine learning (ML).

At first we focus on generating CY manifolds, built as hypersurfaces in toric varieties, with genetic algorithms. We find new examples CY fourfolds with topology distinct from fourfolds in existing datasets. We also use these algorithms to generate CY manifolds that satisfy certain phenomenology constraints.

Knowledge of the Ricci-flat metric on a CY is required to compute particle properties of the resulting four-dimensional effective field theory. Using ML approximations of the metric, we compute the Yukawa couplings arising from the E8 × E8 heterotic string compactified on a CY threefold X with holomorphic vector bundle V by computing the bundle-valued harmonic modes of the Laplacian operator. We consider the particular case where X is a hypersurface in a single ambient space and V is a line bundle sum.

Finally, we build a dataset of G2 manifolds via certain contact CY manifolds, called CY links, and study their topology. We show how neural networks can be used to predict aspects of the topology of these manifolds, namely their Sasakian Hodge number h2,1, from the list of weights w defining the CY link. Using symbolic regression we construct an approximate formula for h2,1 in terms of w. This serves as the first application of ML to G2 geometry.

Keywords: String Theory, Calabi-Yau Manifolds, G2 Manifolds, Machine-Learning, String Compactification

Publication Type:	Thesis (Doctoral)
Subjects:	Q Science > QA Mathematics Q Science > QA Mathematics > QA76 Computer software
Departments:	School of Science & Technology > Mathematics School of Science & Technology > School of Science & Technology Doctoral Theses Doctoral Theses

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