Asymptotic dynamics in perturbative quantum gravity and BMS supertranslations

Abstract

Abstract:Recently it has been shown that infrared divergences in the conventional Smatrix 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 transition induced by the scattering process.

BMS supertranslation symmetry implies Faddeev-Kulish amplitudes

“…Working out the infrared divergences (see [10] for details), we see that they factor out and cancel as…”

“…It will turn out that any amplitude that obeys the conservation law (2.28), an example being (2.32), is equal to the Faddeev-Kulish amplitude and is therefore IR-finite. Before moving on, it is worth noting that the Faddeev-Kulish states of gravity have zero supertranslation charge for the specific choice made in (2.9) (but not for a general function f (z,z), as shown in [9,10]). This is analogous to the case of QED [11], where the corresponding Faddeev-Kulish states have zero large gauge charge for f (z,z) = 1 z−w .…”

“…We follow the shorthand notations used in [10]: 6) and S µν (p, k) = P µν (p, k) + C µν (p, k). These allow us to write, (see [10] for details)…”

“…These are (1) corrections due to virtual graviton exchange, (2) the interacting graviton corrections arising from gravitons connecting the Faddeev-Kulish clouds to external legs, and finally (2) corrections due to cloud-to-cloud graviton exchanges. These have been discussed in detail in appendix B of [10]. Now let us see what happens if we put all the clouds in the outgoing state.…”

“…Again, we begin by considering the individual contributions, i.e., virtual, interacting, and cloud-to-cloud gravitons. The virtual graviton contribution is unchanged from the one given in [10]. For the interacting gravitons, consider the amplitude of a diagram with N (N ) absorbed (emitted) interacting gravitons,…”