Consistency of supersymmetric 't Hooft anomalies

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.

Automated summary

The passage discusses how to remove the anomaly in supersymmetry in the presence of an R-symmetry anomaly and enlarging the corresponding current multiplet. It also explores the additional effects on Ward identities for other existing anomalies when the supersymmetry anomaly is removed. Finally, it validates the modified consistency conditions through explicit computation using Pauli-Villars regulators.