Anomaly puzzle in N=1 supersymmetric electrodynamics as artifact of dimensional reduction

Abstract

Calculations of the two-loop $\beta$-function for N=1 supersymmetric electrodynamics are compared for regularizations by higher derivatives and by the dimensional reduction. The renormalized effective action are found to be the same for both regularizations. However, unlike the dimensional reduction, the higher derivative regularization does not lead to anomaly puzzle, because it allows to perform correct calculation of diagrams with insertions of counterterms. In particular, using this method a contribution of diagrams with insertions of counterterms is calculated exactly to all orders. This contribution appears to be 0 if the theory is regularized by the dimensional reduction. We argue, that this result follows from mathematical inconsistency of the dimensional reduction and is responsible for the anomaly puzzle.

arXiv commentLaTeX, 21 pages, 8 eps figures, corrections in signs, a misprint removed, references added

References in corpus (3)

• Holomorphy, Rescaling Anomalies and Exact beta Functions in Supersymmetric Gauge Theories
• $N=1$ supersymmetry and the three loop anomalous dimension for the chiral superfield
• Two-loop renormalization of N=1 supersymmetric electrodynamics, regularized by higher derivatives

Cited by in corpus (4)

• Three-loop $\beta$-function for N=1 supersymmetric electrodynamics, regularized by higher derivatives
• On the higher-derivative supersymmetric gauge theory
• Universal invariant renormalization of supersymmetric Yang-Mills theory
• New Derivation of Anomaly-Mediated Gaugino Mass in the Higher Derivative Regularization Method