Effects of D-instantons in string amplitudes (original) (raw)

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 α ′ s ≫ 1, fixed scattering angle, and very weak coupling g s ≪ 1/(α ′ 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 α ′ s ≪ 1/ √ g s , the pure D instanton contribution to the scattering amplitude is found to produce a factor A Dinst 4 ∼ = exp(cg 3/2 s e − 2π g s s 3). At energies 1/ √ g s ≪ α ′ s ≪ 1/g s , the D-instanton factor becomes A Dinst 4 ∼ = exp(2e − 2π g s +πg s s 2), α ′ = 4. At higher energies α ′ 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.