Relating the RNS and Pure Spinor Formalisms for the Superstring

TL;DR

This paper establishes a connection between the RNS and pure spinor formalisms for superstrings, enabling translation of physical states and amplitudes, and introduces a $b$ ghost for loop calculations.

Contribution

It provides a field redefinition and similarity transformation that relate the pure spinor BRST operator to the RNS BRST operator plus $ abla$ ghost, facilitating cross-formalism computations.

Findings

Mapped the pure spinor BRST operator to the RNS BRST operator plus $ abla$ ghost.

Related physical vertex operators and tree amplitudes across formalisms.

Indicated the existence of a $b$ ghost in the pure spinor formalism for loop calculations.

Abstract

Recently, the superstring was covariantly quantized using the BRST-like operator $Q = \oint \lambda^\alpha d_\alpha$ where $\lambda^\alpha$ is a pure spinor and $d_\alpha$ are the fermionic Green-Schwarz constraints. By performing a field redefinition and a similarity transformation, this BRST-like operator is mapped to the sum of the Ramond-Neveu-Schwarz BRST operator and $\eta_0$ ghost. This map is then used to relate physical vertex operators and tree amplitudes in the two formalisms. Furthermore, the map implies the existence of a $b$ ghost in the pure spinor formalism which might be useful for loop amplitude computations.