Consistency of supersymmetric 't Hooft anomalies

TL;DR

This paper investigates the consistency of supersymmetric 't Hooft anomalies, demonstrating how to remove supersymmetry anomalies via counterterms, and verifying the modified anomaly conditions through explicit one-loop calculations.

Contribution

It provides an explicit counterterm to remove supersymmetry anomalies and analyzes the impact on current multiplets and Ward identities in supersymmetric theories.

Findings

Supersymmetry anomalies can be removed with explicit counterterms.

Modified Wess-Zumino consistency conditions are satisfied after anomaly removal.

Supersymmetric regularization of correlators is achievable using Pauli-Villars regulators.

Abstract

We consider recent claims that supersymmetry is anomalous in the presence of a R-symmetry anomaly. We revisit arguments that such an anomaly in supersymmetry can be removed and write down an explicit counterterm that accomplishes it. Removal of the supersymmetry anomaly requires enlarging the corresponding current multiplet. As a consequence the Ward identities for other symmetries that are already anomalous acquire extra terms. This procedure can only be impeded when the choice of current multiplet is forced. We show how Wess-Zumino consistency conditions are modified when the anomaly is removed. Finally we check that the modified Wess-Zumino consistency conditions are satisfied, and supersymmetry unbroken, in an explicit one loop computation using Pauli-Villars regulators. To this end we comment on how to use Pauli-Villars to regulate correlators of components of (super)current multiplets in a manifestly supersymmetric way.