Light-Cone Analysis of the Pure Spinor Formalism for the Superstring

TL;DR

This paper presents a light-cone analysis of the pure spinor formalism for superstrings, introducing a similarity transformation that simplifies the BRST charge and connects light-cone and covariant descriptions.

Contribution

It introduces a similarity transformation that simplifies the BRST charge in the pure spinor formalism and relates light-cone and covariant descriptions of superstring states.

Findings

Simplified the form of the BRST charge Q.

Mapped light-cone superstring states to DDF-like operators.

Connected light-cone and covariant formalisms in pure spinor superstring theory.

Abstract

Physical states of the superstring can be described in light-cone gauge by acting with transverse bosonic $\alpha_{-n}^{j}$ and fermionic $\bar{q}_{-n}^{\dot{a}}$ operators on an $SO\left(8\right)$-covariant superfield where $j,\dot{a}=1$ to $8$. In the pure spinor formalism, these states are described in an $SO\left(9,1\right)$-covariant manner by the cohomology of the BRST charge $Q=\frac{1}{2\pi i}\oint\lambda^{\alpha}d_{\alpha}$. In this paper, a similarity transformation is found which simplifies the form of $Q$ and maps the light-cone description of the superstring vertices into DDF-like operators in the cohomology of $Q$.