Effects of D-instantons

TL;DR

The paper analyzes D-instantons in Type IIB theory, deriving nonperturbative corrections to the effective action by integrating fermionic zero modes in both supergravity and string theory backgrounds. It identifies a leading lambda^16 term and an R^4 term, showing how D-instanton effects generate nonperturbative contributions that match between the two descriptions and motivate a modular, SL(2,Z)-invariant completion of the R^4 interaction. The authors propose a concrete f(tau, tau_bar) coefficient for R^4, expressed as an Eisenstein-series-like sum, consistent with perturbative limitations and nonperturbative D-instanton effects, and connect these results to T-duality and M-theory. They furthermore investigate fixed-angle scattering in the D-instanton background, revealing point-like, power-law behavior for certain disk amplitudes and detailing the Dirichlet divergences and their cancellations. Overall, the work links nonperturbative IIB dynamics, duality symmetries, and high-energy scattering, suggesting deep modular structures governing stringy corrections to gravity.

Abstract

Scattering of fundamental states of type IIB supergravity and superstring theory is discussed at low orders in perturbation theory in the background of a D-instanton. The integration over fermionic zero modes in both the low energy supergravity and in the string theory leads to explicit nonperturbative terms in the effective action. These include a single instanton correction to the known tree-level and one-loop $R^4$ interactions. The `spectrum' of multiply-charged D-instantons is deduced by T-duality in nine dimensions from multiply-wound world-lines of marginally-bound D-particles. This, and other clues, lead to a conjectured SL(2,Z) completion of the $R^4$ terms which suggests that they are not renormalized by perturbative corrections in the zero-instanton sector beyond one loop. The string theory unit-charged D-instanton gives rise to point-like effects in fixed-angle scattering, raising unresolved issues concerning distance scales in superstring theory.