Instantons at strong coupling, averaging over vacua, and the gluino condensate

We consider instanton contributions to chiral correlators, such as <0|Tr λ²(x)Tr λ²(x′)|0>, in script N = 1 supersymmetric Yang-Mills theory with either light adjoint or fundamental matter. Within the former model, extraction of the gluino condensate from a connected 1-instanton diagram, evaluated at strong coupling, can be contrasted with expectations from the Seiberg-Witten solution perturbed to an script N = 1 vacuum. We observe a numerical discrepancy, coinciding with that observed previously in script N = 1 SQCD. Moreover, since knowledge of the vacuum structure is complete for softly broken script N = 2 Yang-Mills, this model serves as a counter example to the hypothesis of Amati et al. that 1-instanton calculations at strong coupling can be interpreted as averaging over vacua. Within script N = 1 SQCD, we point out that the connected contribution to the relevant correlators actually vanishes in the weakly coupled Higgs phase, despite having a non-zero value through infra-red effects when calculated in the unbroken phase.