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

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.

9 pages, 3 figures; v2: discussion improved, references updated

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• Classification of Feynman integral geometries for black-hole scattering at 5PM order
• General Relativity from Intersection Theory
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• Quasi-Keplerian parametrization for compact binaries on hyperbolic orbits in scalar-tensor theories at second post-Newtonian order
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• A construction of single-valued elliptic polylogarithms