1995/03/31 by Simon Davis, Davis, Simon
Computer Science · Physics and Astronomy · #Algorithms and Data Compression #Cellular Automata and Applications #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.hep-th/9503231
35 pages, TeX, 2 figures. This is the July version with several typographical corrections and 2 figures included
openalex publication_date 1995/04/01 · arxiv created 1996/04/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The genus-dependence of multi-loop superstring amplitudes is bounded at large orders in perturbation theory using the super-Schottky group parametrization of supermoduli space. Partial estimates of supermoduli space integrals suggest an exponential dependence on the genus when the integration region is restricted to a single fundamental domain of the super-modular group in the super-Schottky parameter space. Bounds for N-point superstring scattering amplitudes are obtained for arbitrary N and are shown to be consistent with exact results recently obtained for special type II string amplitudes for orbifold or Calabi-Yau compactifications. It is suggested that the generic estimates, which imply the validity of superstring perturbation theory in the weak-coupling limit, might be used to determine scattering amplitudes at strong coupling because of the S-duality of type II and heterotic string theories. Non-perturbative effects are consistent with these estimates, based on a sum over closed surfaces, because they can be derived from an additional contribution to the sum over surfaces corresponding to the insertion of Dirichlet boundaries.