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.
Highlights
Quantum effects can make a classical symmetry anomalous
If the current can be extended to a conserved current jmμ in the massive theory in such a way that jmμ = j0μ + O(m), the corresponding symmetry is non-anomalous
If the current j0μ can be extended to the massive theory and the Ward identity holds in the massive theory with the same right hand side, the anomaly is absent
Summary
Quantum effects can make a classical symmetry anomalous. The interplay between anomalies and supersymmetry has long been studied [1,2,3,4,5,6,7]. While supersymmetry can be gauged even in the presence of a U(1) R-anomaly, there are interesting physical consequences of the anomaly of [8,9,10,11,12] These arise when considering supersymmetric field theories on rigid supergravity backgrounds. For instance one can define a supersymmetric index by placing a theory with a U(1) R-symmetry on S3 × S1 preserving supersymmetry and computing its partition function This is accomplished by coupling the theory to an off shell new minimal supergravity background. We show that this anomaly can be removed by introducing a chiral multiplet that plays the role of a compensator for the chiral U(1) R-symmetry and conformal supersymmetry Introducing this compensator is interpreted as coupling the theory to old minimal supergravity. We thank the authors for sharing the draft of their work prior to publication and for illuminating conversations
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