《Solution of the Anomaly Puzzle in SUSY Gauge Theories and the Wilson Operator Expansion》.pdf

Nuclear Physics B277 (1986) 456-486 North-Holland, Amsterdam S O L U T I O N O F T H E A N O M A L Y P U Z Z L E IN S U S Y G A U G E THEORIES AND THE WILSON OPERATOR EXPANSION M.A. SHIFMAN* and A.I. VAINSHTEIN Institute of Nuclear Physics, Novosibirsk 90, USSR Received 23 April 1986 The present paper completes a series of works on fl functions and the anomaly problem in supersymmetric theories. Exact expressions for the fl functions are obtained within the framework of standard perturbation theory. The key observation is that the Wilson effective action Sw(~) does not coincide with the sum of vacuum loops in the external field F(/O. The difference is due to infrared effects. The coefficient 1 / g 2 in front of the operator W2 in Sw 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 5iln Z i where the factors Zi 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. 1. Introduction It is well-known that the perturbative series in supersymmetric (SUSY) models [1] possess miraculous properties. Thus, for F terms the loop