Fractional superstrings with space-time critical dimensions four and six.

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. String theories[1] are primarily characterized by the local symmetries of a twodimensional field theory on the string world-sheet. The local symmetries of the bosonic string are reparameterization and Weyl invariance which lead to a critical string propagating in 26 flat space-time dimensions. The superstring enlarges the world-sheet gauge invariance to include a local N = 1 supersymmetry, and reduces the critical space-time dimension to 10. It is natural to try to construct string theories with smaller critical space-time dimensions by changing the worldsheet symmetry. Unfortunately, enlarging to a local N = 2 supersymmetry produces a critical string in just two-dimensional Minkowski space. It is well known, however, that fractionalspin fields can exist in two-dimensional field theory. One can imagine new local symmetries on the world-sheet which involve fractional-spin currents and which lead to string propagation in space-times with dimensions less than 10. In this letter we will present evidence for the existence of such new string theories, and in particular will show that strings with spin 4/3 and 6/5 currents on the world-sheet can have interesting phenomenologies in 6 and 4 space-time dimensions, respectively. The algebra of constraints resulting from gauge-fixing the two-dimensional local symmetry must contain the Virasoro algebra. In this letter we consider strings with