The Superembedding Origin of the Berkovits Pure Spinor Covariant Quantization of Superstrings

TL;DR

This paper reveals that Berkovits' pure spinor formalism for superstring quantization is a gauge-fixed, twisted version of the superembedding approach, providing geometric insights and clarifying its ghost structure.

Contribution

It establishes a geometric origin for the pure spinor formalism by linking it to the superembedding formulation, and clarifies its ghost and BRST structure.

Findings

Pure spinor formalism is a gauge-fixed superembedding version.

The approach is geometrically superdiffeomorphism invariant.

Relation between Green-Schwarz and pure spinor formalisms is clarified.

Abstract

We show that the pure spinor formalism proposed by Berkovits to covariantly quantize superstrings is a gauge fixed, twisted version of the complexified n=2 superembedding formulation of the superstring. This provides the Berkovits approach with a geometrical superdiffeomorphism invariant ground. As a consequence, the absence of the worldsheet (super)diffeomorphism ghosts in the pure spinor quantization prescription and the nature of the Berkovits BRST charge and antighost are clarified. Since superembedding is classically equivalent to the Green-Schwarz formulation, we thus also relate the latter to the pure spinor construction.