  Mason and Skinner proposed the ambitwistor string theory which directly
reproduces the formulas for the amplitudes of massless particles proposed by
Cachazo, He and Yuan. In this paper we discuss geometries of the moduli space
of worldsheets associated to the bosonic or the RNS ambitwistor string.
Further, we investigate the factorization properties of the amplitudes when an
internal momentum is near on-shell in the abstract CFT language. Along the way,
we propose the existence of the ambitwistor strings with three or four
fermionic worldsheet currents.
