Ambitwistor strings at null infinity and (subleading) soft limits

The relationship between BMS symmetries at null infinity and Weinberg's soft theorems for gravitons and photons together with their subleading extensions are developed using ambitwistor string theory. Ambitwistor space is the phase space of complex null geodesics in complexified space-time. We show how it can be canonically identified with the cotangent bundle of complexified null infinity. BMS symmetries of null infinity lift to give a Hamiltonian action on ambitwistor space, both in general dimension and in its twistorial four-dimensional representation. General vertex operators arise from Hamiltonians generating diffeomorphisms of ambitwistor space that determine the scattering from past to future null infinity. When a momentum eigenstate goes soft, the diffeomorphism defined by its leading and its subleading part are extended BMS generators realized in the world sheet conformal field theory of the ambitwistor string. More generally, this gives an explicit perturbative correspondence between the scattering of null geodesics and that of the gravitational field via ambitwistor string theory.