Collinear and Soft Divergences in Perturbative Quantum Gravity

TL;DR

This work analyzes infrared divergences in perturbative quantum gravity for fixed-angle scattering. It develops a power-counting framework to identify collinear and soft divergences, proving that collinear singularities cancel when all relevant diagrams are summed via the gravitational Ward identity, and that soft divergences arise only from ladder-type exchanges and can be described by Wilson lines in the eikonal limit. The main contributions are the generalization of collinear cancellation to arbitrary orders and the confirmation that soft divergences are restricted to ladder-type diagrams, highlighting a key difference from gauge theories. The findings advance understanding of gravity's infrared structure and have potential implications for high-energy scattering analyses and nonperturbative considerations.

Abstract

Collinear and soft divergences in perturbative quantum gravity are investigated to arbitrary orders in amplitudes for wide-angle scattering, using methods developed for gauge theories. We show that collinear singularities cancel when all such divergent diagrams are summed over, by using the gravitational Ward identity that decouples the unphysical polarizations from the S-matrix. This analysis generalizes a result previously demonstrated in the eikonal approximation. We also confirm that the only virtual graviton corrections that give soft logarithmic divergences are of the ladder and crossed ladder type.

Figures (12)

• Figure 1: A general reduced diagram at the pinched singular point. J and S denote the jet and soft subdiagrams and H is a hard vertex. Here each line may represent any number of soft propagators connecting S to the remainder of the diagram, or the jets J${}_i$ to the hard part H.
• Figure 2: A diagram with a graviton jet attached to an external leg. We show the case where there are two gravitons being emitted from the external line and two gravitons attaching to "rest" but these can be any numbers. The analysis in section \ref{['sec:jet']} shows that the number of gravitons emitted and attached do not need to be the same.
• Figure 3: A typical ladder diagram.
• Figure 4: A diagram with no internal jet loops and only three point vertices.
• Figure 5: An example of an external leg correction. These do not result in collinear singularities.