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Non-Perturbative Effects in Superstring and Yang--Mills Theory
Michael Green
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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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hep-th/9712195,**hep-th/9804170**,**hep-th/9807033**
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