Effects of D-instantons in string amplitudes

We investigate the different energy regimes in the conjectured SL(2, Z) invariant four graviton scattering amplitude that incorporates D-instanton contributions in 10d type IIB superstring theory. We show that the infinite product over SL(2, Z) rotations is convergent in the whole complex plane s, t. For high energies alpha's >> 1, fixed scattering angle, and very weak coupling g(s) << 1/(alpha's), the four-graviton amplitude exhibits the usual exponential suppression. As the energy approaches 1/g(s), the suppression gradually diminishes until there appears a strong amplification near a new pole coming from the exchange of a (p, q) string. At energies alpha's << 1/root g(s), the pure D-instanton contribution to the scattering amplitude is found to produce a factor A(4)(D-inst) congruent to exp(cg(s)(3/2)e (-2 pi/gs) s(3)). At energies 1/root g(s) << alpha's << 1/g(s), the D-instanton factor becomes A(4)(D-inst) congruent to exp(2e (-2 pi/gs + pi gss2)), alpha' = 4. At higher energies alpha's >> 1/g(s) the D-instanton contribution becomes very important, and one finds an oscillatory behavior which alternates suppression and amplification. This suggests that non-perturbative effects can lead to a high-energy behavior which is significantly different from the perturbative string behavior. (c) 2005 Elsevier B.V. All rights reserved.