Frellesvig Hjalte, Morales Roger, Wilhelm Matthias
Niels Bohr International Academy, Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark.
Mani L. Bhaumik Institute for Theoretical Physics, University of California at Los Angeles, Los Angeles, California 90095, USA.
Phys Rev Lett. 2024 May 17;132(20):201602. doi: 10.1103/PhysRevLett.132.201602.
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.
我们研究了费曼积分中出现的几何结构，这些结构在后闵可夫斯基（PM）展开中对黑洞散射有贡献。通过经典保守势，这些几何结构与双黑洞合并产生的引力波相关。在四圈阶（4PM），已知一个K3曲面出现在一个三圈积分中，导致结果中出现椭圆积分。在本论文中，我们在一个四圈积分中识别出一个卡拉比-丘三维流形，它在五圈阶（5PM）有贡献。这种卡拉比-丘几何结构的存在表明，在完整的解析结果中出现了全新的函数。
