## Abstract

The present paper completes a series of works on β functions and the anomaly problem in supersymmetric theories. Exact expressions for the β functions are obtained within the framework of standard perturbation theory. The key observation is that the Wilson effective action S_{W}(μ) does not coincide with the sum of vacuum loops in the external field Γ(μ). The difference is due to infrared effects. The coefficient 1/g^{2} in front of the operator W^{2} in S_{W} is renormalized only at one-loop level (extension of the non-renormalization theorem for F-terms). This fact results in the one-loop form of the anomalous operator equation for the supercurrent (generalization of the Adler-Bardeen theorem). The full Gell-Mann-Low function emerges after passing to matrix elements of the operators. The quantity entering observable amplitudes differs from 1/g^{2} by Σ_{i}lnZ_{i} where the factors Z_{i} describe renormalization of the fields. (In this sense the Z factors of the matter fields become observable.) We discuss the relation with calculations of the instanton type.

Original language | English (US) |
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Pages (from-to) | 456-486 |

Number of pages | 31 |

Journal | Nuclear Physics, Section B |

Volume | 277 |

Issue number | C |

DOIs | |

State | Published - 1986 |

Externally published | Yes |