Generalized Unitarity Method for Worldline Field Theory

TL;DR

The paper addresses the challenge of computing classical gravitational observables from worldline field theories without gauge redundancies or Feynman diagrams. It introduces a generalized unitarity framework that constructs perturbative worldline observables from locality and unitarity, using complexified worldline energies and on-shell factorization. The authors bootstrap rational worldline amplitudes from local building blocks, then extend to loop-like integrands via maximal cuts, applying the method to reproduce the on-shell action and the gravitational waveform at ${O}(G^{5/2})$, matching known results. The work promises a streamlined path for analyzing compact binaries and motivates extensions to spinning worldlines and double-copy structures.

Abstract

We present a generalized unitarity method for theories of point-particle worldlines coupled to gravity, analogous to that of scattering amplitudes in quantum field theory. This method allows the computation of perturbative observables from basic principles such as locality and unitarity, thus avoiding gauge redundancies and the use of Feynman diagrams. We illustrate the method with a variety of examples, including the gravitational waveform for the scattering of two point masses at next-to-leading order (or ${\cal O}(G^{5/2})$), reproducing known results. Our method further streamlines the calculation of the scattering dynamics of compact binary systems and opens the door to further applications and systematical exploration of structure in this class of observables.

Figures (7)

• Figure 1: Schwinger-Keldysh contour for in-in correlators.
• Figure 2: The amplitudes factorize into products of sub-amplitudes upon cutting an internal propagator. Wavy lines represent gravitons and thick solid lines represent worldline fluctuations.
• Figure 3: Factorization of worldline amplitudes upon cutting the complex energies. The thick solid lines represent worldline fluctuations with real (thus vanishing) energy and the thick dashed lines represent worldline fluctuations with complexified energy. In all our diagrams, we assign the conjugate energy to the sub-amplitude on the right.
• Figure 4: The cut topologies for $\mathcal{A}(h_1,h_2,h_3)$ with the cut-collapsing procedure. In our terminology, the arrows point from the parent topology to the child topology.
• Figure 5: Maximal cut topologies for the waveform.