Cohomology in the Pure Spinor Formalism for the Superstring

TL;DR

This paper demonstrates that the cohomology of the BRST operator in the pure spinor formalism reproduces the superstring spectrum, linking covariant quantization with the light-cone Green-Schwarz approach.

Contribution

It shows the BRST cohomology in the pure spinor formalism yields the superstring spectrum, clarifying the role of the Virasoro constraint.

Findings

BRST cohomology matches light-cone Green-Schwarz spectrum

Virasoro constraint emerges from pure spinor variables

Covariant formalism simplifies superstring quantization

Abstract

A manifestly super-Poincar\'e covariant formalism for the superstring has recently been constructed using a pure spinor variable. Unlike the covariant Green-Schwarz formalism, this new formalism is easily quantized with a BRST operator and tree-level scattering amplitudes have been evaluated in a manifestly covariant manner. In this paper, the cohomology of the BRST operator in the pure spinor formalism is shown to give the usual light-cone Green-Schwarz spectrum. Although the BRST operator does not directly involve the Virasoro constraint, this constraint emerges after expressing the pure spinor variable in terms of SO(8) variables.