Calabi-Yau Meets Gravity: A Calabi-Yau Threefold at Fifth Post-Minkowskian Order
Hjalte Frellesvig, Roger Morales, Matthias Wilhelm
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.
Topics & Concepts
Calabi–Yau manifoldPhysicsOrder (exchange)Mathematical physicsGravitational wavePure mathematicsClassical mechanicsQuantum mechanicsMathematicsFinanceEconomicsPulsars and Gravitational Waves ResearchBlack Holes and Theoretical PhysicsCosmology and Gravitation Theories