Construction of an asymptotic S matrix for perturbative quantum gravity

TL;DR

The paper formulates an IR-finite S matrix for perturbative quantum gravity by extending the Faddeev–Kulish approach to gravity, constructing an asymptotic operator that dresses external states with soft graviton clouds. It shows that soft divergences cancel to all orders in gravitational potential scattering and connects the soft sector to gravitational Wilson lines, yielding an explicit all-orders exponentiation. The framework preserves gauge and Lorentz invariance and yields physically meaningful, exclusive amplitudes without relying on cross-section summations. The results illuminate the infrared structure of gravity, link to asymptotic symmetries, and provide a solid foundation for perturbative analyses in gravity and supergravity contexts.

Abstract

The infrared behavior of perturbative quantum gravity is studied using the method developed for QED by Faddeev and Kulish. The operator describing the asymptotic dynamics is derived and used to construct an IR-finite S matrix and space of asymptotic states. All-orders cancellation of IR divergences is shown explicitly at the level of matrix elements for the example case of gravitational potential scattering. As a practical application of the formalism, the soft part of a scalar scattering amplitude is related to the gravitational Wilson line and computed to all orders.

Figures (8)

• Figure 1: An diagram with a graviton jet attached to an external leg.
• Figure 2: A diagram with no internal jet loops and only three point vertices.
• Figure 3: Arbitrary diagram with virtual soft graviton corrections to a hard vertex. The finite momentum lines are drawn with a solid line.
• Figure 4: An example of the type of diagram discussed in section \ref{['sec:soft']}. Here $L_{S}=4$, $N_{S}=8$, and $N_{E}$=4.
• Figure 5: An example of a diagram with only three point couplings to hard lines that will lead to a soft divergence.