Non-Perturbative Effects in Superstring and Yang--Mills Theory
Michael Green
This talk surveys some higher derivative terms in the effective IIB superstring action that can be expressed as integrals over half the on-shell superspace and whose form is known exactly. Examples are the (Weyl tensor)**4 term and the sixteen-dilatino term, each of which is multiplied by an exactly determined nonholomorphic modular form which depends on the complex scalar field. The expansion for small exp**phi has no perturbative contributions beyond one loop and an infinite series of D-instanton terms, with fluctuations at all orders around each instanton. The charge-K D-instanton measure is related to the bulk contribution to the Witten index for K D-particles in the IIA theory and has a form that is suggests the presence of threshold bound states. Upon compactifying on AdS5 X S5 these IIB interactions are translated into exact non-perturbative statements in maximally supersymmetric four-dimensional SU(N) Yang--Mills theory at order N**(-3/2) in the large-N limit. A correspondence between the classical D-instanton of the bulk IIB theory and the Yang--Mills instanton is demonstrated and some instanton dominated Yang--Mills correlation functions are compared with D-instanton amplitudes in IIB supergravity.

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