From 4d ambitwistor strings to on shell diagrams and back

We investigate the relation between 4d ambitwistor string theory and on-shell diagrams for planar N = 4 super-Yang-Mills and N = 8 supergravity, and deduce several new results about their scattering amplitudes at tree-level and 1-loop. In particular, we derive new Grassmannian integral formulae for tree-level amplitudes and obtain new world-sheet formulae for 1-loop amplitudes which are manifestly supersymmetric and supported on scattering equations refined by MHV degree.