Effects of D-instantons in string amplitudes

Abstract

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 s>> 1, fixed scattering angle, and very weak coupling g<< 1/s, the four-graviton amplitude exhibits the usual exponential suppression. As the energy approaches 1/g, 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 s<< 1/\sqrt{g}, the pure D instanton contribution to the scattering amplitude is found to produce a factor $A_4^{Dinst}\cong \exp (c{g}^{3/2}{e}^{-\frac{2\pi }{g}}{s}^3)$. At energies $1/\sqrt{g}<<s<<1/g$, the D-instanton factor becomes $A_4^{Dinst}\cong \exp (2e^{-\frac{2\pi }{g_s}+\pi g_s{s}^2})$. At higher energies s>> 1/g 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.

11 pages, 3 figures

References in corpus (1)

• String-theoretic unitary S-matrix at the threshold of black-hole production

Cited by in corpus (1)

• Normalization of Type IIB D-instanton Amplitudes