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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. NSFNational Science Foundation (NSF) [PHY-1720321] W.C. and J.G. would like to thank M. Headrick for valuable discussions. The work of W.C. and J.G. is supported in part by NSF grant PHY-1720321. The authors would like to gratefully acknowledge the Simons Center for Geometry and Physics (and the semester long program, The Geometry and Physics of Hitchin Systems) for hospitality during the completion of this work. |
