General Relativity from Intersection Theory and Loop Integrals

TL;DR

This paper introduces a novel application of intersection theory to compute gravitational scattering amplitudes in quantum gravity, specifically for black hole interactions at the second Post-Minkowskian order, providing a new mathematical framework.

Contribution

It is the first to apply intersection theory to quantum gravity calculations, offering a new method for analyzing Feynman integrals in gravitational scattering.

Findings

Successfully computed 2PM correction coefficients using intersection theory.

Results agree with existing literature on gravitational scattering amplitudes.

Introduced twisted (co)-homology groups to quantum gravity calculations.

Abstract

The study investigates the gravitational scattering amplitude between two Schwarzschild black holes in a two to two interaction, focusing on the Second Post-Minkowskian correction (2 PM). Analyzing contributions from box and cross-box diagrams, the research interprets Feynman integrals as pairings between twisted co-cycles and cycles. The concept of twisted (co)-homology groups is introduced, leading to a master integral decomposition formula. The study successfully applies intersection theory to compute coefficients of the master integral basis, marking the first application of intersection theory in the quantum field theoretic description of gravity. The results align with existing literature on the 2PM correction.