SUMMABILITY OF SUPERSTRING THEORY

Abstract. Several arguments are given for the summability of the superstring perturbation series. Whereas the Schottky group coordinatization of moduli space may be used to provide refined estimates of large-order bosonic string amplitudes, the super-Schottky group variables define a measure for the supermoduli space integral which leads to upper bounds on superstring scattering amplitudes. The genus-dependence of superstring amplitudes have been estimated recently using the super-Schottky coordinatization of supermoduli space. The N-point g-loop amplitudes in Type IIB superstring theory have been found to grow exponentially with the genus,