Not So Flat Metrics

TL;DR

This paper improves the large volume approximation in string compactifications by using machine learning to obtain numerical Calabi-Yau metrics and studies the impact of $oldsymbol{eta'}^3$ corrections on the scalar Laplacian spectrum, relevant for string phenomenology.

Contribution

It introduces a machine learning approach to estimate numerical Calabi-Yau metrics and incorporates $oldsymbol{eta'}^3$ corrections, enhancing the accuracy of string compactification models.

Findings

Improved estimates of large volume approximation using ML-derived metrics

Quantified the impact of $oldsymbol{eta'}^3$ corrections on the scalar Laplacian spectrum

Highlighted the significance of higher derivative corrections for realistic string models

Abstract

In order to be in control of the $\alpha'$ derivative expansion, geometric string compactifications are understood in the context of a large volume approximation. In this letter, we consider the reduction of these higher derivative terms, and propose an improved estimate on the large volume approximation using numerical Calabi-Yau metrics obtained via machine learning methods. Further to this, we consider the $\alpha'^3$ corrections to numerical Calabi-Yau metrics in the context of IIB string theory. This correction represents one of several important contributions for realistic string compactifications -- alongside, for example, the backreaction of fluxes and local sources -- all of which have important consequences for string phenomenology. As a simple application of the corrected metric, we compute the change to the spectrum of the scalar Laplacian.