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arXiv · hep-th/0506129

Numerical Ricci-flat metrics on K3

Matthew Headrick·Toby Wiseman
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Abstract

We develop numerical algorithms for solving the Einstein equation on Calabi-Yau manifolds at arbitrary values of their complex structure and Kahler parameters. We show that Kahler geometry can be exploited for significant gains in computational efficiency. As a proof of principle, we apply our methods to a one-parameter family of K3 surfaces constructed as blow-ups of the T^4/Z_2 orbifold with many discrete symmetries. High-resolution metrics may be obtained on a time scale of days using a desktop computer. We compute various geometric and spectral quantities from our numerical metrics. Using similar resources we expect our methods to practically extend to Calabi-Yau three-folds with a high degree of discrete symmetry, although we expect the general three-fold to remain a challenge due to memory requirements.

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Matthew Headrick, Toby Wiseman. 2006-04-03. Numerical Ricci-flat metrics on K3. https://doi.org/10.1088/0264-9381%2F22%2F23%2F002

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