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Feynman diagrams have been superseded as the tool of choice for calculatingscattering amplitudes. Various other methods are not only more efficient butalso explicitly exhibit beautiful structures obscured by Feynman diagrams. Thisthesis aims to lay some groundwork on how two of these methods, ambitwistorstrings and the double copy, can be generalised to scattering in curvedbackgrounds. In the first part of this thesis, a heterotic ambitwistor stringmodel coupled to a non-abelian background gauge field is constructed. It isshown that after decoupling gravity this model is anomaly free if and only ifthe background field is a solution to the Yang-Mills equations. A fixed gluonvertex operator for the aforementioned heterotic model as well as a vertexoperator encoding graviton, B-field and dilaton for type II ambitwistor stringsin a curved background are presented. It is shown that they are BRST closed ifand only if they correspond to physical on-shell states. In the second part,sandwich plane waves are considered. It is shown that scattering of gluons andgravitons is well defined on these backgrounds. 3-point amplitudes arecalculated using quantum field theory techniques and a double copy relationbetween gluons on a gauge theory plane wave and gravitons on a gravitationalplane wave is proposed. Using the results from the first part of this thesis,it is then shown that curved background heterotic and type II ambitwistorstring models correctly reproduce these 3-point amplitudes on sandwich planewaves.

Ambitwistor strings and amplitudes in curved backgrounds