Moduli-dependent Calabi-Yau and SU(3)-structure metrics from Machine Learning

TL;DR

This paper employs machine learning to efficiently approximate Calabi-Yau and SU(3)-structure metrics, incorporating complex structure moduli dependence, with significant improvements in accuracy and computational speed, impacting string theory and mirror symmetry research.

Contribution

Introduces a machine learning approach to compute moduli-dependent metrics on Calabi-Yau and SU(3)-structure manifolds, enhancing accuracy and efficiency over previous methods.

Findings

Successfully models complex structure moduli dependence.

Achieves improved accuracy and speed in metric approximation.

Demonstrates methods on quintic hypersurfaces in projective space.

Abstract

We use machine learning to approximate Calabi-Yau and SU(3)-structure metrics, including for the first time complex structure moduli dependence. Our new methods furthermore improve existing numerical approximations in terms of accuracy and speed. Knowing these metrics has numerous applications, ranging from computations of crucial aspects of the effective field theory of string compactifications such as the canonical normalizations for Yukawa couplings, and the massive string spectrum which plays a crucial role in swampland conjectures, to mirror symmetry and the SYZ conjecture. In the case of SU(3) structure, our machine learning approach allows us to engineer metrics with certain torsion properties. Our methods are demonstrated for Calabi-Yau and SU(3)-structure manifolds based on a one-parameter family of quintic hypersurfaces in $\mathbb{P}^4.$