On pure spinor formalism for quantum superstring and spinor moving frame

TL;DR

This paper reformulates the pure spinor formalism for the quantum superstring using spinor moving frame variables, aiming for a more complete and potentially more useful description of the measure in the path integral.

Contribution

It introduces a new reformulation of the pure spinor superstring using spinor moving frame variables and Cartan forms, providing a potentially complete set of variables.

Findings

Reformulation of the pure spinor measure in terms of Cartan forms.

Relation of spinor variables to kappa-symmetry ghosts.

Potential for a complete reformulation of the superstring theory.

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.