Twistor/ambitwistor strings and null-superstrings in spacetime of D=4,10 and 11 dimensions

We show that, at the classical level, the recently proposed `ambitwistor string' model is equivalent to the spinor moving frame formulation of null-supersting, which in its turn is equivalent to Siegel's formulation of closed twistor string or to its higher dimensional generalizations. Although the null-(super)string is usually considered as describing the tensionless limit of (super)string, we show that its action can be derived from the spinor moving frame formulation of superstring also in the infinite tension limit. This observation allows us to argue on the absence of critical dimensions and suggests that the (ambi)twistor string based technique(s) to calculate field theory amplitudes can be developed not only in D=10 or 26, but also in D=11 and other dimensions. The D=11 and D=10 twistor strings are described in some details.