Supersymmetric instanton calculus. Gauge theories with matter

Within the framework of gauge SUSY theories we discuss correlation functions of the type 〈W²(x), S²(0)〉 where S is the chiral matter superfield (in the one-flavor model). SUSY implies that these correlation functions do not depend on coordinates and vanish identically in perturbation theory. We develop a technique for the systematic calculation of instanton effects. It is shown that even in the limit x→0 the correlation functions at hand are not saturated by small-size instantons with radius θ∼x; a contribution of the same order of magnitude comes from the instantons of characteristic size θ∼1/ν (ν is the vacuum expectation value of the scalar field, and we concentrate on the models with ν≫Λ where Λ is the scale parameter fixing the running gauge coupling constant). If ν≫Λ both types of instantons can be consistently taken into account. The computational formalism proposed is explicitly supersymmetric and uses the language of instanton-associated superfields. We demonstrate, in particular, that one can proceed to a new variable, ρ{variant}_inv, which can be naturally considered as a supersymmetric generalization of the instanton radius. Unlike the ordinary radius ρ{variant}, this variable is invariant under the SUSY transformations. If one uses ρ{variant}_inv instead of ρ{variant} the expressions for the instanton contribution can be rewritten in the form saturated by the domain ρ{variant}_inv²=0. The cluster decomposition as well as x-independence of the correlation functions considered turn out to be obvious in this formalism.