Abstract
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.
Highlights
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
The null-(super)string is usually considered as describing the tensionless limit ofstring, we show that its action can be derived from the spinor moving frame formulation of superstring in the infinite tension limit
In this paper we show that, at the classical level, the ambitwistor string model is equivalent to null- superstring as described in moving frame and spinor moving frame formulation
Summary
The action for bosonic ‘ambitwistor string’ proposed by Mason and Skinner in [1] reads. We just consider the above discussion as a suggestion that, upon a suitable use of an additional dimensional constant (which is certainly present in the models of interest for the ambitwistor string program) the infinite tension limit of classical GS superstring can be described by the null-superstring action. As it was shown in [42], the D=4 N = 4 version of the twistor-like formulation of nullsuperstring [10,11,12,13] is equivalent to the closed twistor string action proposed by Siegel in [43] (see [44] for original formulation and [45] for an alternative action for twistor string) This gives one more indirect argument in favor of our conjecture on the absence of critical dimension for the infinite tension limit of superstring, as on one hand, according to section 3, it can be described using the null-superstring action, and, on the other hand, twistor string is known to give a consistent (anomaly free) theory in D=4. The D-dimensional null-superstring actions can be written starting form the spinor moving frame formulations of the massless superparticle actions presented in [47] for D=4, in [48] for D=3, 4, 6 and 10 and in [49,50,51,52] for D=11
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