Relating the Green-Schwarz and Pure Spinor Formalisms for the Superstring

TL;DR

This paper demonstrates the equivalence between BRST quantization of the Green-Schwarz superstring in semi-light-cone gauge and the pure spinor formalism, bridging two approaches to superstring quantization.

Contribution

It establishes a formal connection between the Green-Schwarz and pure spinor formalisms through BRST quantization equivalence.

Findings

BRST quantization of GS superstring in semi-light-cone gauge is equivalent to pure spinor formalism.

Provides a covariant quantization approach for the GS superstring.

Bridges two major superstring quantization frameworks.

Abstract

Although it is not known how to covariantly quantize the Green-Schwarz (GS) superstring, there exists a semi-light-cone gauge choice in which the GS superstring can be quantized in a conformally invariant manner. In this paper, we prove that BRST quantization of the GS superstring in semi-light-cone gauge is equivalent to BRST quantization using the pure spinor formalism for the superstring.