Origin of Pure Spinor Superstring

TL;DR

This paper derives the pure spinor superstring formalism from a fundamental, fully quantum, reparametrization invariant worldsheet action, establishing its equivalence to the Green-Schwarz formalism and justifying the use of free fields.

Contribution

It provides a first-principles derivation of the pure spinor superstring formalism, extending the Green-Schwarz action with doubled spinor degrees of freedom and local supersymmetry.

Findings

Pure spinor formalism derived at quantum level

Equivalence to Green-Schwarz formalism established

Justification for use of free fields from first principles

Abstract

The pure spinor formalism for the superstring, initiated by N. Berkovits, is derived at the fully quantum level starting from a fundamental reparametrization invariant and super-Poincare invariant worldsheet action. It is a simple extension of the Green-Schwarz action with doubled spinor degrees of freedom with a compensating local supersymmetry on top of the conventional kappa-symmetry. Equivalence to the Green-Schwarz formalism is manifest from the outset. The use of free fields in the pure spinor formalism is justified from the first principle. The basic idea works also for the superparticle in 11 dimensions.