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.
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