Graviton scattering in self-dual radiative space-times

Abstract

We give formulae for all tree-level graviton scattering amplitudes in curved self-dual radiative space-times; these are chiral, source-free, asymptotically flat spaces determined by free characteristic data at null infinity. Such space-times admit an elegant description in terms of twistor theory and Penrose's non-linear graviton, which manifests their underlying integrability. The tree-level S-matrix is written in terms of an integral over the moduli space of holomorphic maps from the Riemann sphere to twistor space, with the degree of the map corresponding to the helicity configuration of the external gravitons. For the MHV sector, we derive the amplitude directly from general relativity, while other helicity configurations arise from a natural family of generating functionals and pass several consistency checks. The amplitudes in self-dual radiative space-times exhibit many novel features which are absent in Minkowski space, including tail effects. There are also residual integrals due to the functional degrees of freedom in the background space-time, although our formulae have fewer such integrals than expected from space-time perturbation theory. In highly symmetric special cases, such as self-dual plane waves, the number of residual integrals can be further reduced, resulting in even simpler expressions for the scattering amplitudes.

The 4d/2d correspondence in twistor space and holomorphic Wilson lines

“…Heuristically, in these backgrounds only the dotted spinors are curved, while the undotted ones remain the same. Amplitudes in these backgrounds still have MHV prefactors [56,57] which foreshadows the existence of a 4d/2d correspondence continues to hold in certain curved backgrounds.…”

Classical physics from amplitudes on curved backgrounds

“…Beyond 3-points, explicit calculations for amplitudes in the background field formalism become increasingly difficult. However, all-multiplicity formulae for scattering amplitudes in chiral plane wave backgrounds have recently been found with twistor methods [70][71][72], showing that there is scope for studying high-order radiation effects with this formalism.…”

An Ambitwistor for Kerr I: Zig-Zag Symplectic Perturbation Theory

“…Arbitrary wave profile In a strict sense, the scattering problem is not well-defined with (3.44) because the oscillation of the wave does not die off at the past and future timelike infinities. A generic self-dual plane wave with an arbitrary profile is given by [175][176][177]…”