Classical and quantum gravitational scattering with Generalized Wilson Lines

Abstract

The all-order structure of scattering amplitudes is greatly simplified by the use of Wilson line operators, describing eikonal emissions from straight lines extending to infinity. A generalization at subleading powers in the eikonal expansion, known as Generalized Wilson Line (GWL), has been proposed some time ago, and has been applied both in QCD phenomenology and in the high energy limits of gravitational amplitudes. In this paper we revisit the construction of the scalar gravitational GWL starting from first principles in the worldline formalism. We identify the correct Hamiltonian that leads to a simple correspondence between the soft expansion and the weak field expansion. This allows us to isolate the terms in the GWL that are relevant in the classical limit. In doing so we devote special care to the regularization of UV divergences that were not discussed in an earlier derivation. We also clarify the relation with a parallel body of work that recently investigated the classical limit of scattering amplitudes in gravity in the worldline formalism.

Light bending from eikonal in worldline quantum field theory

“…Our dressed propagator can also be applied to the description of light by light scattering, and it would be interesting to study amplitudes made up of dressed photon propagators in the case where the spin tensor contributes. Another interesting route would be to explore the so-called generalized Wilson line [63][64][65][66] for photons. Dressed photon propagators are also useful in describing the propagation of light in an arbitrary medium [67] so it would be interesting to consider coupling to matter in addition to gravity.…”

The Uncertainty Principle and Classical Amplitudes

“…This amounts to saying that the amplitude is described by a vacuum expectation value of Wilson line operators, which is by no means a new observation: the description of the Regge (high energy) limit of 2 → 2 scattering in terms of Wilson lines was given in QCD [84], and later generalised to gravity in [61,88] (see also refs. [107,108]). The QED case, however, is particularly simple.…”