Fractional superstrings with space-time critical dimensions four and six

Abstract
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≥2 an integer. We present evidence for their existence by constructing modular-invariant partition functions and the massless particle spectra. The dimension 4 and 6 strings have space-time supersymmetry.