Consistency of supersymmetric 't Hooft anomalies

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.

arXiv comment47 pages + appendices; v2: typos fixed, references added

References in corpus (16)

• Comments on Supercurrent Multiplets, Supersymmetric Field Theories and Supergravity
• The Geometry of Supersymmetric Partition Functions
• Supercurrents and Brane Currents in Diverse Dimensions
• Two-dimensional gravitational anomalies, Schwinger terms and dispersion relations
• Renormalised 3-point functions of stress tensors and conserved currents in CFT
• Supercurrent anomalies in 4d SCFTs
• Pauli-Villars Regularization of Supergravity Coupled to Chiral and Yang-Mills Matter
• The holographic supersymmetric Casimir energy
• 't Hooft anomalies and the holomorphy of supersymmetric partition functions
• Supersymmetry anomalies in $\mathcal{N}=1$ conformal supergravity
• Anomalous Supersymmetry
• TripleK: A Mathematica package for evaluating triple-K integrals and conformal correlation functions
• Comments on Anomalies in Supersymmetric Theories
• Pauli-Villars Regularization of Globally Supersymmetric Theories
• Supersymmetry anomalies in new minimal supergravity
• Quantum consistency in supersymmetric theories with $R$-symmetry in curved space

Cited by in corpus (6)

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• Deformations of Supergravity and Supersymmetry Anomalies
• Anomalies and Supersymmetry