Renormalization of Supersymmetric Field Theories in Loop Regularization with String-mode Regulators

TL;DR

This paper applies Loop Regularization with string-mode regulators to supersymmetric theories, explicitly verifying Ward identities and demonstrating that the method preserves supersymmetry and gauge symmetry at one-loop level, including in the Wess-Zumino model.

Contribution

It introduces a novel regularization scheme that maintains supersymmetry and gauge invariance in supersymmetric field theories at one-loop level.

Findings

Supersymmetric Ward identities hold with LR in four-dimensional space-time.

Quadratic divergences cancel in the Wess-Zumino model after renormalization.

Relations among masses and couplings are preserved, consistent with non-renormalization theorems.

Abstract

By applying the recently developed Loop Regularization(LR) with string-mode regulators to supersymmetric field theories, we explicitly verify the supersymmetric Ward identities in several supersymmetric models at one-loop level. It is interesting to observe that supersymmetry is a so remarkable symmetry that the supersymmetric Ward identities hold as long as a regularization scheme is realized in the exact four dimensional space-time with translational invariance for the momentum integration, and the gauge symmetry can be maintained once the regularization scheme preserves supersymmetry and satisfies the consistency condition for logarithmic divergences. As a manifest demonstration, we carry out a complete one-loop renormalization for the massive Wess-Zumino model by adopting the LR method, it is found that all the quadratic divergences cancel out and the relations among masses and coupling constants hold after renormalization, which agrees with the well-known non-renormalization theorem. It is concluded that the LR method preserves not only gauge symmetry but also supersymmetry. A simple and definite derivation of Majorana Feynman rules is found to be very useful.