Consistent Momentum Space Regularization/Renormalization of Supersymmetric Quantum Field Theories: The 3-loop beta function for the Wess-Zumino Model

TL;DR

This paper calculates the three-loop beta function of the Wess-Zumino model to demonstrate the effectiveness of implicit regularization in handling supersymmetric quantum field theories within momentum space.

Contribution

It introduces implicit regularization as a consistent, practical momentum-space method for studying supersymmetric quantum field theories and their anomalies.

Findings

Ultraviolet divergences are clearly separated from infrared divergences.

The method yields consistent results supporting its use in supersymmetry studies.

Motivates IR as a good framework for supersymmetry anomaly analysis.

Abstract

We compute the three loop $\beta$ function of the Wess-Zumino model to motivate implicit regularization (IR) as a consistent and practical momentum-space framework to study supersymmetric quantum field theories. In this framework which works essentially in the physical dimension of the theory we show that ultraviolet are clearly disantangled from infrared divergences. We obtain consistent results which motivate the method as a good choice to study supersymmetry anomalies in quantum field theories.