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Numerical Metrics for Complete Intersection and Kreuzer-Skarke Calabi-Yau Manifolds

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arxiv 2205.13408 v1 pith:CDNKOLZL submitted 2022-05-26 hep-th

Magdalena Larfors , Andre Lukas , Fabian Ruehle , Robin Schneider This is my paper
classification hep-th
keywords manifoldskreuzer-skarkelinemanifoldmetricsahlerbi-cubicbundle
verification ladder T0 review T1 audit T2 compute T3 formal
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We introduce neural networks to compute numerical Ricci-flat CY metrics for complete intersection and Kreuzer-Skarke Calabi-Yau manifolds at any point in K\"ahler and complex structure moduli space, and introduce the package cymetric which provides computation realizations of these techniques. In particular, we develop and computationally realize methods for point-sampling on these manifolds. The training for the neural networks is carried out subject to a custom loss function. The K\"ahler class is fixed by adding to the loss a component which enforces the slopes of certain line bundles to match with topological computations. Our methods are applied to various manifolds, including the quintic manifold, the bi-cubic manifold and a Kreuzer-Skarke manifold with Picard number two. We show that volumes and line bundle slopes can be reliably computed from the resulting Ricci-flat metrics. We also apply our results to compute an approximate Hermitian-Yang-Mills connection on a specific line bundle on the bi-cubic.

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Cited by 5 Pith papers

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