  The relationships between extended BMS symmetries at null infinity and
Weinberg's soft theorems for gravitons and photons together with their
subleading generalizations 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 null infinity. BMS symmetries of null infinity lift to give a
hamiltonian action on ambitwistor space, both in general dimension and in its
twistorial 4-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 explicit perturbative
correspondence between the scattering of null geodesics and that of the
gravitational field via ambitwistor string theory.
