Supercurrent anomaly and gauge invariance in N=1 supersymmetric Yang-Mills theory

TL;DR

This paper investigates the quantum breaking of supercurrent conservation in N=1 supersymmetric Yang-Mills theory, clarifying longstanding controversies about anomalies and gauge invariance using specific regularization methods.

Contribution

It provides a detailed analysis of supercurrent anomalies in supersymmetric Yang-Mills theory, highlighting the role of regularization and momentum routing in anomaly evaluation.

Findings

Superconformal symmetry is unambiguously broken with invariant four-dimensional regularization.

The study clarifies the connection between supercurrent anomaly and the triangle AVV anomaly.

Subtleties in loop momentum routing affect the evaluation of Feynman diagrams.

Abstract

We analyse Feynman diagram calculational issues related to the quantum breaking of supercurrent conservation in a supersymmetric non-abelian Yang-Mills theory. For the sake of simplicity, we take a zero mass gauge field multiplet interacting with a massless Majorana spin-$1/2$ field in the adjoint representation of $SU(2)$. We shed light on a long-standing controversy regarding the perturbative evaluation of the supercurrent anomaly in connection with gauge and superconformal symmetry in different frameworks. We find that only superconformal symmetry is unambiguously broken using an invariant four dimensional regularization and compare with the triangle AVV anomaly. Subtleties related to momentum routing invariance in the loops of diagrams and Clifford algebra evaluation inside divergent integrals are also discussed in connection with finite and undetermined quantities in Feynman amplitudes.