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arXiv · 2312.11371

Calabi-Yau meets Gravity: A Calabi-Yau three-fold at fifth post-Minkowskian order

Hjalte Frellesvig·Roger Morales·Matthias Wilhelm
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Abstract

We study geometries occurring in Feynman integrals that contribute to the scattering of black holes in the post-Minkowskian expansion. These geometries become relevant to gravitational-wave production during the inspiralling phase of binary black hole mergers through the classical conservative potential. At fourth post-Minkowskian order, a K3 surface is known to occur in a three-loop integral, leading to elliptic integrals in the result. In this letter, we identify a Calabi-Yau three-fold in a four-loop integral, contributing at fifth post-Minkowskian order. The presence of this Calabi-Yau geometry indicates that completely new functions occur in the full analytical results at this order.

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Hjalte Frellesvig, Roger Morales, Matthias Wilhelm. 2023-12-18. Calabi-Yau meets Gravity: A Calabi-Yau three-fold at fifth post-Minkowskian order. https://doi.org/10.1103/physrevlett.132.201602

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