On pure spinor formalism for quantum superstring and spinor moving frame

Abstract

The D=10 pure spinor constraint can be solved in terms of spinor moving frame variables and 8-component complex null vector which can be related to the kappa-symmetry ghost. Using this and similar solutions for the conjugate pure spinor and other elements of the non-minimal pure spinor formalism we present a (hopefully useful) reformulation of the measure of the pure spinor path integral for superstring in terms of products of Cartan form corresponding to the coset of 10D Lorentz group and to the coset of complex orthogonal group SO(8,C). Our study suggests a possible complete reformulation of the pure spinor superstring in terms of new irreducible set of variable.