Equivalence Proof of Pure Spinor and Ramond-Neveu-Schwarz Superstring Amplitudes

TL;DR

This paper establishes the equivalence between the pure spinor and Ramond-Neveu-Schwarz superstring amplitude formalisms, introducing a new covariant prescription that simplifies computations and maintains supersymmetry.

Contribution

It provides a new manifestly spacetime-supersymmetric pure spinor formalism related by a field redefinition to the RNS formalism, clarifying their equivalence.

Findings

Pure spinor and RNS formalisms are equivalent for superstring amplitudes.

The new prescription avoids subtleties from pure spinor ghost poles.

For certain amplitudes, the new prescription reduces to previous pure spinor methods.

Abstract

A new manifestly spacetime-supersymmetric prescription for superstring amplitude computations is given using the pure spinor formalism which does not contain subtleties from poles in the pure spinor ghosts. This super-Poincare covariant prescription is related by a U(5)-covariant field redefinition to the Ramond-Neveu-Schwarz amplitude prescription where the pure spinor parameterizes the choice of SO(10)/U(5). For F-term scattering amplitudes which preserve a subset of the spacetime supersymmetries, the new pure spinor amplitude prescription reduces to the previous pure spinor prescription.