The Polyakov Approach and Divergences in Open Superstrings

String theories have, recently re-emerged, pheonix-like, into the mainstream of particle physics. The principal reasons for this revival are threefold: Superstrings are believed to be renormalizable (possibly even finite), unitary, theories that include gravity as well as the usual gauge and matter interactions [1,2,30,33,34].Strings ‘miraculously’ satisfy very stringent requirements of mathematical consistency [2,3,4]. These requirements arise in the form of anomaly-cancellation conditions and are sufficiently restrictive that only a handful (Type I, Types IIa, IIb, and heterotic with gauge groups E8 x E8 or Spin(32)/Z2) of candidate string theories survive.Finally, the Type I and heterotic strings appear to have the potential of producing a realistic phenomenology at energies low enough (i. e. E “ Mp) to be accessible to experiment [5]. (For a review see L. Ibáñez, this volume.)