TY - JOUR

T1 - Supersymmetric instanton calculus. Gauge theories with matter

AU - Novikov, V. A.

AU - Shifman, M. A.

AU - Vainshtein, A. I.

AU - Zakharov, V. I.

PY - 1985/10/14

Y1 - 1985/10/14

N2 - 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.

AB - 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.

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U2 - 10.1016/0550-3213(85)90316-5

DO - 10.1016/0550-3213(85)90316-5

M3 - Article

AN - SCOPUS:0009044541

SN - 0550-3213

VL - 260

SP - 157

EP - 181

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 1

ER -