Twistor-like superstrings with D = 3, 4, 6 target-superspace and N = (1,0), (2,0), (4,0) world-sheet supersymmetry

TL;DR

This paper develops a new twistor-like superstring formulation with enhanced world-sheet supersymmetry in six dimensions, incorporating Grassmann analyticity, and explores its symmetry structure and relation to simpler models.

Contribution

It introduces a manifestly N=(4,0) supersymmetric twistor-like formulation of the D=6 superstring using harmonic superspace and identifies its symmetry properties.

Findings

Constructed a D=6 superstring action with N=(4,0) supersymmetry.

Identified kappa symmetry as a Kac-Moody extension of superconformal symmetry.

Extended the formulation to include world-sheet reparametrization symmetry.

Abstract

We construct a manifestly $N=(4,0)$ world-sheet supersymmetric twistor-like formulation of the $D=6$ Green-Schwarz superstring, using the principle of double (target-space and world-sheet) Grassmann analyticity. The superstring action contains two Lagrange multiplier terms and a Wess-Zumino term. They are written down in the analytic subspace of the world-sheet harmonic $N=(4,0)$ superspace, the target manifold being too an analytic subspace of the harmonic $D=6\;\; N=1$ superspace. The kappa symmetry of the $D=6$ superstring is identified with a Kac-Moody extension of the world-sheet $N=(4,0)$ superconformal symmetry. It can be enlarged to include the whole world-sheet reparametrization group if one introduces the appropriate gauge Beltrami superfield into the action. To illustrate the basic features of the new $D=6$ superstring construction, we first give some details about the simpler (already known) twistor-like formulations of $D=3, N=(1,0)$ and $D=4, N=(2,0)$ superstrings.