TY - JOUR

T1 - Graviton scattering in self-dual radiative space-times

AU - Adamo, Tim

AU - Mason, Lionel

AU - Sharma, Atul

N1 - Funding Information:
We would like to thank Harry Braden for interesting conversations about graph theory and Maciej Dunajski for many helpful discussions and comments. T A is supported by a Royal Society University Research Fellowship and by the Leverhulme Trust (RPG-2020-386). L J M is grateful to the STFC for support under Grant ST/T000864/1. A S is supported by a Mathematical Institute Studentship, Oxford and by the ERC Grant GALOP ID: 724638.
Publisher Copyright:
© 2023 The Author(s). Published by IOP Publishing Ltd.

PY - 2023/5/4

Y1 - 2023/5/4

N2 - The construction of amplitudes on curved space-times is a major challenge, particularly when the background has non-constant curvature. We give formulae for all tree-level graviton scattering amplitudes in curved self-dual (SD) 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, which provides the powerful tools required to exploit 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 the Einstein-Hilbert action of general relativity, while other helicity configurations arise from a natural family of generating functionals and pass several consistency checks. The amplitudes in SD radiative space-times exhibit many novel features that are absent in Minkowski space, including tail effects. There remain residual integrals due to the functional degrees of freedom in the background space-time, but our formulae have many fewer such integrals than would be expected from space-time perturbation theory. In highly symmetric special cases, such as SD plane waves, the number of residual integrals can be further reduced, resulting in much simpler expressions for the scattering amplitudes.

AB - The construction of amplitudes on curved space-times is a major challenge, particularly when the background has non-constant curvature. We give formulae for all tree-level graviton scattering amplitudes in curved self-dual (SD) 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, which provides the powerful tools required to exploit 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 the Einstein-Hilbert action of general relativity, while other helicity configurations arise from a natural family of generating functionals and pass several consistency checks. The amplitudes in SD radiative space-times exhibit many novel features that are absent in Minkowski space, including tail effects. There remain residual integrals due to the functional degrees of freedom in the background space-time, but our formulae have many fewer such integrals than would be expected from space-time perturbation theory. In highly symmetric special cases, such as SD plane waves, the number of residual integrals can be further reduced, resulting in much simpler expressions for the scattering amplitudes.

KW - graviton scattering

KW - QFT in curved spacetime

KW - scattering amplitudes

KW - self-duality

KW - twistor theory

UR - http://www.scopus.com/inward/record.url?scp=85151491098&partnerID=8YFLogxK

U2 - 10.1088/1361-6382/acc233

DO - 10.1088/1361-6382/acc233

M3 - Article

AN - SCOPUS:85151491098

SN - 0264-9381

VL - 40

JO - Classical and quantum gravity

JF - Classical and quantum gravity

IS - 9

M1 - 095002

ER -