FRACTIONAL SUPERSTRINGS WITH SPACE-TIME CRITICAL DIMENSION-4 AND DIMENSION-6

We propose possible new string theories based on local world-sheet symmetries corresponding to extensions of the Virasoro algebra by fractional-spin currents. They have critical central charges c = 6(K + 8)/(K + 2) and Minkowski space-time dimensions D = 2 + 16/K for K greater-than-or-equal 2 an integer. We present evidence for their existence by constructing modular-invariant partition functions and the mass-less particle spectra. The dimension 4 and 6 strings have space-time supersymmetry.