Aspects of scattering amplitudes: on strong backgrounds and in twistor space

Abstract

In this thesis we study the properties of scattering amplitudes in two contexts: in the presence of strong background fields; and their twistorial representations.

In the first part, we consider scattering amplitudes in strong background fields: classical solutions of the equations of motion which are treated non-perturbatively. Our focus is on highly symmetric, but physically relevant, plane wave and spherically symmetric backgrounds. In the case of plane waves, we review the calculation and properties of these amplitudes. For spherically symmetric backgrounds we propose a semi-classical approximation to the solutions of the equations of motion that is well-suited to amplitude calculations. Thus, we obtain the first expression for semi-classical 3-point amplitudes in Coulomb and Schwarzschild backgrounds.

Amplitudes on backgrounds are of particular interest due to their applications in computing classical observables such as gravitational waveforms arising from astrophysical phenomena. We conclude the first part by using amplitudes on plane wave backgrounds to calculate the classical radiation waveform of scattering events on these backgrounds.

In the second part, we explore aspects of tree-level amplitudes formulated as localised integrals over the moduli space of maps to twistor space. These are representations closely related to twistor string theory that provide all-multiplicity closed-form expressions for scattering amplitudes in gauge theory and gravity, graded by the helicity of the external particles.

A remarkable aspect of amplitudes in gauge theory and gravity is that they are related via the double copy. In the final section of this thesis, we study how these twistor space representations of amplitudes manifest the double copy via applications of graph theory. In doing so, we find new twistorial representations of biadjoint scalar amplitudes. Connecting to the first part of this thesis, amplitudes on certain self-dual backgrounds in gauge theory and gravity also enjoy all-multiplicity representations as moduli space integrals of maps to twistor space. Generalising these arguments, we make the first step towards an all-multiplicity statement of the double copy for amplitudes on self-dual backgrounds.