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.

arXiv comment9 pages, 3 figures; v2: discussion improved, references updated

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• Classifying post-Minkowskian geometries for gravitational waves via loop-by-loop Baikov
• Three-loop banana integrals with four unequal masses
• SOFIA: Singularities of Feynman Integrals Automatized
• Bootstrapping spinning two body problem in dynamical Chern-Simons gravity using worldline QFT
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• General Relativity from Intersection Theory
• Canonical differential equations and intersection matrices
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• The spectrum of Feynman-integral geometries at two loops
• A construction of single-valued elliptic polylogarithms