New critical dimensions for string theories

Abstract

The open string dynamics which include the Liouville field theory following Polyakov and Gervais-Neveu are shown to enjoy the same remarkable properties as the celebrated string theories in D = 26 or D = 10 dimensions, provided D is changed to D = 7 or 13 for the purely bosonic string and to D = 3 or 5 for superstrings. For these new critical dimensions all four models have a free open string partition function which is such that the closed string singularities in the one-loop open string amplitude are poles. For superstrings, the partition functions in the Neveu-Schwarz and Ramond sectors are shown to coincide after the appropriate GOS projection has been carried out, and the new models are presumably space-time supersymmetric. These new critical dimensions are, in each model, the lowest two of the three special values already derived by Gervais and Neveu from their study of the Liouville dynamics per se.