Ambitwistor string amplitudes in light-like linear dilaton background

Using the ambitwistor string theory, we study graviton scattering amplitudes in a light-like linear dilaton background of 10-dimensional supergravity. At tree level, find that three-graviton amplitude coincides with type-II superstring and four-graviton or more differ from theory but satisfy equations. Due to modified momentum conservation law different at each order genus expansion, nonzero is determined solely particular perturbation without further corrections.