Phys. Rev. Lett. 132, 201602 (2024) - Calabi-Yau Meets Gravity: A Calabi-Yau Threefold at Fifth Post-Minkowskian Order
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Calabi-Yau Meets Gravity: A Calabi-Yau Threefold at Fifth Post-Minkowskian Order

Hjalte Frellesvig, Roger Morales, and Matthias Wilhelm
Phys. Rev. Lett. 132, 201602 – Published 15 May 2024
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Abstract

We study geometries occurring in Feynman integrals that contribute to the scattering of black holes in the post-Minkowskian (PM) expansion. These geometries become relevant to gravitational-wave production from binary mergers through the classical conservative potential. At 4PM, 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 threefold in a four-loop integral, contributing at 5PM. The presence of this Calabi-Yau geometry indicates that completely new functions occur in the full analytical results.

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  • Received 16 January 2024
  • Accepted 8 April 2024

DOI:https://doi.org/10.1103/PhysRevLett.132.201602

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Classical black holesGravitational wavesPerturbation theoryQuantum field theoryScattering amplitudes
Particles & Fields

Authors & Affiliations

Hjalte Frellesvig1, Roger Morales1,2, and Matthias Wilhelm1

  • 1Niels Bohr International Academy, Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark
  • 2Mani L. Bhaumik Institute for Theoretical Physics, University of California at Los Angeles, Los Angeles, California 90095, USA

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Issue

Vol. 132, Iss. 20 — 17 May 2024

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  • Figure 1
    Figure 1

    (a) Kinematics of the scattering process, exemplified by the tree-level diagram. The arrows indicate the direction of the momenta, thin and thick lines, respectively, denote the graviton and scalar matter propagators. (b) A Feynman diagram containing a Calabi-Yau threefold.

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  • Figure 2
    Figure 2

    Simplifying relations for the geometries in PM Feynman integrals: (a) the vertices at matter lines become effectively orderless; (b) dangling triangles have vanishing leading singularities.

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  • Figure 3
    Figure 3

    The Mondrian family of Feynman diagrams.

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