Asymptotic Dynamics in Perturbative Quantum Gravity and BMS Supertranslations

TL;DR

The paper addresses IR divergences in perturbative quantum gravity by employing FK asymptotic states and analyzing their behavior under BMS supertranslations. By computing the BMS charge of FK-dressed states, it shows that these charges label superselection sectors and are conserved, implying no transitions between sectors and that the FK graviton clouds implement the necessary vacuum transitions during scattering. The analysis demonstrates a precise cancellation between the BMS action on bare particles and on their graviton clouds, yielding IR-finite S-matrix elements and a clean vacuum structure shaped by BMS symmetry. This work solidifies the connection between asymptotic symmetries and the IR problem in gravity and clarifies how soft gravitons encode vacuum degeneracy and selection rules in scattering processes.

Abstract

Recently it has been shown that infrared divergences in the conventional S-matrix elements of gauge and gravitational theories arise from a violation of the conservation laws associated with large gauge symmetries. These infrared divergences can be cured by using the Faddeev-Kulish (FK) asymptotic states as the basis for S-matrix elements. Motivated by this connection, we study the action of BMS supertranslations on the FK asymptotic states of perturbative quantum gravity. We compute the BMS charge of the FK states and show that it characterizes the superselection sector to which the state belongs. Conservation of the BMS charge then implies that there is no transition between different superselection sectors, hence showing that the FK graviton clouds implement the necessary vacuum transition induced by the scattering process.

Figures (6)

• Figure 1: Diagrams illustrating the causal structure of Minkowski spacetime, reproduced from Strominger:2017zoo. Left: the green lines describe hypersurfaces of constant $\rho$, and the grey line is the world-line of a massive particle moving at a constant velocity. Right: hyperbolic slicing of Minkowski spacetime. The slices correspond to constant $\tau$ hypersurfaces, where for $\tau^2>0$ the resulting surface is the hyperbolic space $\mathbb{H}_3$ and for $\tau^2<0$ it is $\mathrm{dS}_3$.
• Figure 2: Different ways to connect an external soft graviton to a scattering amplitude. The first two diagrams on the left represent a soft graviton that is connected to an external leg. The last two diagrams on the right represent a soft graviton that is connected to the gravitons' cloud. The diagram in the middle represents a soft graviton that is connected to an internal leg.
• Figure 3: Contributions of a virtual graviton.
• Figure 4: Contributions of interacting gravitons.
• Figure 5: Contributions of cloud-to-cloud gravitons.