MSc Defense by Toni Teschke

Title: One Loop Scalar Gravitational Scattering via Intersection Theory

Abstract: In this work we examine the gravitational scattering amplitude involving two Schwarzshild black holes as massive scalars in a 2 -> 2 interaction. Specifically we focus on the Second Post-Minkowski correction (2PM). We find that Feynman Integrals, represented in Baikov form, can naturally be represented as a pairing between a twisted co-cycle and a twisted cycle.

We introduce the concept of twisted (co)-homology groups and explore the notion of an intersection number, which quantifies the pairing between elements of the twisted co-homology group and their dual counterparts.

This insight leads us to the development of a master decomposition formula, demonstrating that the intersection number acts as scalar product in the space of Feynman Integrals. We present a recursive algorithm for computing that quantity, and provide a comprehensive example.

Furthermore we use the algorithm of multivariate intersection theory to determine the coefficients of the master integral bases for the box and cross-box contributions. Finally we evaluate the master integrals and their coefficients in the classical limit.
This demonstrates for the first time the applicability of intersection theory in the quantum field theoretic description of gravity.

Supervisor: Hjalte Axel Frellesvig