D-instanton induced interactions on a D3-brane

Non-perturbative features of the derivative expansion of the effective acti on of a single D3-brane are obtained by considering scattering amplitudes o f open and closed strings. This motivates expressions for the coupling cons tant dependence of world-volume interactions of the form (partial derivativ e F)(4) (where F is the Born-Infeld field strength), (partial derivative(2) phi)(4) (where phi are the normal coordinates of the D3-brane) and other in teractions related by N = 4 supersymmetry. These include terms that transfo rm with non-trivial modular weight under Montonen-Olive duality. The leadin g D-instanton contributions that enter into these effective interactions ar e also shown to follow from an explicit stringy construction of the moduli space action for the D-instanton/D3-brane system in the presence of D3-bran e open-string sources (but in the absence of a background antisymmetric ten sor potential). Extending this action to include closed-string sources lead s to a unified description of non-perturbative terms in the effective actio n of the form (embedding curvature)(2) together with open-string interactio ns that describe contributions of the second fundamental form.