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Instantons, Compactification and S-duality in N=4 SUSY Yang-Mills Theory II

We present a semiclassical calculation of instanton effects in N=4 supersymmetric Yang-Mills theory formulated on R^{3}XS^{1} and also in the N=1 theory obtained by introducing chiral multiplet masses. In the N=4 case, these instanton effects are related to the bulk contribution to the index which counts BPS dyons in the corresponding four dimensional theory. In both cases, the calculations provide semiclassical tests of recently proposed exact results for the lowest non-trivial terms in the derivative expansion of the Wilsonian effective action.