TWISTOR-LIKE SUPERSTRINGS WITH D=3,4,6 TARGET SUPERSPACE AND N=(1,0),(2,0),(4,0) WORLD-SHEET SUPERSYMMETRY

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.