  We describe new ambitwistor string theories that give rise to the recent
amplitude formulae for Einstein-Yang-Mills, (Dirac)-Born-Infeld, Galileons and
others introduced by Cachazo, He and Yuan. In the case of the
Einstein-Yang-Mills amplitudes, an important role is played by a novel
worldsheet conformal field theory that provides the appropriate colour factors
precisely without the spurious multitrace terms of earlier models that had to
be ignored by hand. This is needed to obtain the correct multitrace terms that
arise when Yang-Mills is coupled to gravity.
