Calabi-Yau metrics, CFTs and random matrices

TL;DR

This paper reviews recent advances in numerically approximating Calabi-Yau metrics, enabling the computation of Laplacian spectra and revealing unexpected connections to random matrix theory.

Contribution

It introduces a numerical approach to approximate Calabi-Yau metrics and demonstrates a novel link between these metrics and random matrix theory.

Findings

Numerical methods can approximate Calabi-Yau metrics effectively.

Spectral data from these metrics can be computed.

A surprising connection to random matrix theory is observed.

Abstract

Calabi-Yau manifolds have played a key role in both mathematics and physics, and are particularly important for deriving realistic models of particle physics from string theory. Unfortunately, very little is known about the explicit metrics on these spaces, leaving us unable, for example, to compute particle masses or couplings in these models. We review recent progress in this direction on using numerical approximations to compute the spectrum of the Laplacian on these spaces. We give an example of what one can do with this new "data", giving a surprising link between Calabi-Yau metrics and random matrix theory.