Numerical Metrics, Curvature Expansions and Calabi-Yau Manifolds

TL;DR

This paper explores how numerical methods can effectively identify regions of high curvature on Calabi-Yau manifolds, which is crucial for validating curvature expansions in string theory.

Contribution

It demonstrates the efficiency of numerical techniques in detecting localized high-curvature regions on Calabi-Yau manifolds, aiding in the study of their geometric properties.

Findings

Numerical methods can reliably identify highly curved regions.

Control of curvature hierarchies is feasible with these techniques.

Numerical approaches complement analytical methods in string theory research.

Abstract

We discuss the extent to which numerical techniques for computing approximations to Ricci-flat metrics can be used to investigate hierarchies of curvature scales on Calabi-Yau manifolds. Control of such hierarchies is integral to the validity of curvature expansions in string effective theories. Nevertheless, for seemingly generic points in moduli space it can be difficult to analytically determine if there might be a highly curved region localized somewhere on the Calabi-Yau manifold. We show that numerical techniques are rather efficient at deciding this issue.