A twistor formulation of the heterotic D=10 superstring with manifest (8,0) worldsheet supersymmetry

TL;DR

This paper introduces a new twistor-based formulation of the heterotic D=10 superstring that maintains manifest supersymmetry and reparametrisation invariance, utilizing auxiliary fields and spinor variables to clarify fermionic symmetry origins.

Contribution

It presents a novel twistor formulation of the heterotic superstring with manifest symmetries and a finite auxiliary field set, elucidating the origin of fermionic kappa symmetry.

Findings

The formulation is manifestly invariant under target-space and worldsheet supersymmetry.

It employs twistor variables parametrizing the sphere S^8 as a coset of the D=10 Lorentz group.

String tension appears only on-shell as an integration constant.

Abstract

We propose a new formulation of the heterotic $D=10$ Green-Schwarz superstring whose worldsheet is a superspace with two even and eight odd coordinates. The action is manifestly invariant under both target-space supersymmetry and a worldsheet reparametrisation supergroup. It contains only a finite set of auxiliary fields. The key ingredient are the commuting spinor (twistor) variables, which naturally arise as worldsheet superpartners of the target space Grassmann coordinates. These spinors parametrise the sphere $S^8$ regarded as a coset space of the $D=10$ Lorentz group. The sphere is associated with the lightlike vector of one of the string Virasoro constraints. The origin of the on-shell $D=10$ fermionic kappa symmetry of the standard Green-Schwarz formulation is explained. An essential and unusual feature is the appearance of the string tension only on shell as an integration constant.