Differential Renormalization of the Wess-Zumino Model

TL;DR

This paper applies differential renormalization to the Wess-Zumino model, successfully computing the three-loop beta function and verifying the Callan-Symanzik equations, demonstrating advantages over other supersymmetric renormalization methods.

Contribution

It is the first application of differential renormalization to the Wess-Zumino model, providing explicit three-loop calculations and highlighting its benefits over existing superspace techniques.

Findings

Beta function computed to three loops, matching previous results.

Callan-Symanzik equations verified at three loops.

Differential renormalization avoids ambiguities of other supersymmetric regulators.

Abstract

We apply the recently developed method of differential renormalization to the Wess-Zumino model. From the explicit calculation of a finite, renormalized effective action, the $\beta$-function is computed to three loops and is found to agree with previous existing results. As a further, nontrivial check of the method, the Callan-Symanzik equations are also verified to that loop order. Finally, we argue that differential renormalization presents advantages over other superspace renormalization methods, in that it avoids both the ambiguities inherent to supersymmetric regularization by dimensional reduction (SRDR), and the complications of virtually all other supersymmetric regulators.