Description
The detection of gravitational waves from coalescing binary systems requires increasingly accurate theoretical description of the gravitational dynamics. In the inspiral regime, the conservative dynamics can be described within an effective field theory framework, where the two-body interactions are treated perturbatively in the post-Newtonian expansion and reformulated in terms of Feynman diagrams.
One of the main challenges in determining higher-order corrections is the appearance of multi-loop
massless two-point Feynman integrals.
In this talk, I will discuss recent developments leading to the determination of static gravitational interactions
at sixth and seventh post-Newtonian order, where six- and seven-loop Feynman integrals arise.
Multi-loop techniques for integral reduction and evaluation, including integration-by-parts identities
and numerical methods, play a central role in obtaining these results.
These developments pave the way toward the completion of the conservative dynamics at these orders and beyond.