Lorentz-Covariant Green-Schwarz Superstring Amplitudes

TL;DR

This paper constructs Lorentz-covariant generators and vertex operators for Green-Schwarz superstring amplitudes, enabling manifestly covariant expressions of scattering amplitudes that were previously gauge-fixed and less transparent.

Contribution

It introduces explicit Lorentz-covariant super-Poincaré generators and vertex operators for superstring amplitudes, improving the covariance of previous gauge-fixed formulations.

Findings

Constructed Lorentz-covariant super-Poincaré generators.

Expressed scattering amplitudes in manifestly covariant notation.

Enhanced the theoretical framework for superstring amplitude calculations.

Abstract

In a recent paper, the BRST formalism for the gauge-fixed N=2 twistor-string was used to calculate Green-Schwarz supersring scattering amplitudes with an arbitrary number of loops and external massless states. Although the gauge-fixing procedure preserved the worldsheet N=2 superconformal invariance of the twistor-string, it broke the target-space SO(9,1) super-Poincar\'e invariance down to an SU(4)xU(1) subgroup. In this paper, generators for the SO(9,1) super-Poincar\'e transformations, as well as manifestly covariant vertex operators, are explicitly constructed out of the gauge-fixed matter fields. The earlier calculated amplitudes are then expressed in manifestly Lorentz-covariant notation.