  In marked contrast to conventional string theory, ambitwistor strings remain
solvable worldsheet theories when coupled to curved background fields. We use
this fact to consider the quantization of ambitwistor strings on plane wave
metric and plane wave gauge field backgrounds. In each case, the worldsheet
model is anomaly free as a consequence of the background satisfying the field
equations. We derive vertex operators (in both fixed and descended picture
numbers) for gravitons and gluons on these backgrounds from the worldsheet CFT,
and study the 3-point functions of these vertex operators on the Riemann
sphere. These worldsheet correlation functions reproduce the known results for
3-point scattering amplitudes of gravitons and gluons in gravitational and
gauge theoretic plane wave backgrounds, respectively.
