Approximate Ricci-flat Metrics for Calabi-Yau Manifolds
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915350598123520 |
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| author | Lee, Seung-Joo Lukas, Andre |
| author_facet | Lee, Seung-Joo Lukas, Andre |
| contents | We outline a method to determine analytic Kähler potentials with associated approximately Ricci-flat Kähler metrics on Calabi-Yau manifolds. Key ingredients are numerically calculating Ricci-flat Kähler potentials via machine learning techniques and fitting the numerical results to Donaldson's Ansatz. We apply this method to the Dwork family of quintic hypersurfaces in $\mathbb{P}^4$ and an analogous one-parameter family of bi-cubic CY hypersurfaces in $\mathbb{P}^2\times\mathbb{P}^2$. In each case, a relatively simple analytic expression is obtained for the approximately Ricci-flat Kähler potentials, including the explicit dependence on the complex structure parameter. We find that these Kähler potentials only depend on the modulus of the complex structure parameter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15766 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximate Ricci-flat Metrics for Calabi-Yau Manifolds Lee, Seung-Joo Lukas, Andre High Energy Physics - Theory Machine Learning Differential Geometry We outline a method to determine analytic Kähler potentials with associated approximately Ricci-flat Kähler metrics on Calabi-Yau manifolds. Key ingredients are numerically calculating Ricci-flat Kähler potentials via machine learning techniques and fitting the numerical results to Donaldson's Ansatz. We apply this method to the Dwork family of quintic hypersurfaces in $\mathbb{P}^4$ and an analogous one-parameter family of bi-cubic CY hypersurfaces in $\mathbb{P}^2\times\mathbb{P}^2$. In each case, a relatively simple analytic expression is obtained for the approximately Ricci-flat Kähler potentials, including the explicit dependence on the complex structure parameter. We find that these Kähler potentials only depend on the modulus of the complex structure parameter. |
| title | Approximate Ricci-flat Metrics for Calabi-Yau Manifolds |
| topic | High Energy Physics - Theory Machine Learning Differential Geometry |
| url | https://arxiv.org/abs/2506.15766 |