Numerical Metrics, Curvature Expansions and Calabi-Yau Manifolds

Understand

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.