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

TL;DR

This paper compares two regularization methods in N=1 supersymmetric electrodynamics, revealing that the higher derivative regularization avoids the anomaly puzzle present in dimensional reduction by allowing correct diagram calculations.

Contribution

It demonstrates that higher derivative regularization provides consistent two-loop beta-function calculations and resolves the anomaly puzzle caused by dimensional reduction.

Findings

Higher derivative regularization yields the same effective action as dimensional reduction.

It allows exact calculation of counterterm diagrams to all orders.

Dimensional reduction's inconsistency leads to the anomaly puzzle.

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.