Lorentz Invariance of the Pure Spinor BRST Cohomology for the Superstring

TL;DR

This paper proves the Lorentz invariance of the pure spinor BRST cohomology in superstring theory by explicitly constructing the SO(9,1) Lorentz generators using an SO(8) parameterization.

Contribution

It provides an explicit construction of Lorentz generators in the pure spinor formalism, confirming Lorentz invariance of the BRST cohomology.

Findings

Lorentz invariance of the pure spinor BRST cohomology is established.

Explicit SO(9,1) Lorentz generators are constructed.

The cohomology coincides with the light-cone Green-Schwarz spectrum.

Abstract

In a previous paper, the BRST cohomology in the pure spinor formalism of the superstring was shown to coincide with the light-cone Green-Schwarz spectrum by using an SO(8) parameterization of the pure spinor. In this paper, the SO(9,1) Lorentz generators are explicitly constructed using this SO(8) parameterization, proving the Lorentz invariance of the pure spinor BRST cohomology.