The Ten-Dimensional Green-Schwarz Superstring is a Twisted Neveu-Schwarz-Ramond String

TL;DR

This paper demonstrates that the ten-dimensional Green-Schwarz superstring can be viewed as a twisted version of the Neveu-Schwarz-Ramond string, establishing an equivalence that simplifies multiloop amplitude calculations while maintaining spacetime supersymmetry.

Contribution

It shows the N=2 Green-Schwarz superstring action is equivalent to a twisted NSR string, providing a new perspective and simplifying multiloop amplitude computations.

Findings

The N=2 stress-energy tensor can be constructed from NSR stress-energy and ghosts.

A field redefinition relates GS matter fields to NSR matter and ghost fields.

Multiloop amplitudes are easier to compute in the GS formalism due to manifest supersymmetry.

Abstract

An action for the ten-dimensional Green-Schwarz superstring with N=2 worldsheet superconformal invariance has recently been used to calculate superstring scattering amplitudes and prove their finiteness. In this paper, it is shown that the N=2 stress-energy tensor for this Green-Schwarz action can be constructed out of the stress-energy tensor and ghosts of the Neveu- Schwarz-Ramond action by the standard twisting procedure. In other words, a field redefinition is found from the GS matter fields into the NSR matter and ghost fields which transforms the matter part of the two fermionic GS super- conformal generators into the $b$ ghost and shifted BRST current of the NSR string. In light-cone gauge, this field redefinition reduces to the usual one relating the light-cone GS and NSR fields. Although this proves the equivalence of physical vertex operators in the two superstring formalisms, multiloop amplitudes are easier to calculate using the Green-Schwarz formalism since manifest spacetime supersymmetry eliminates the need for spin cuts, GSO projections, and cutoffs in moduli space.