Supersymmetry anomalies in new minimal supergravity

Abstract

We determine the general structure of quantum anomalies for the $R$-multiplet of four dimensional $\mathcal{N}=1$ supersymmetric quantum field theories in the presence of background fields for an arbitrary number of Abelian flavor multiplets. By solving the Wess-Zumino consistency conditions for off-shell new minimal supergravity in four dimensions with an arbitrary number of Abelian vector multiplets, we compute the anomaly in the conservation of the supercurrent to leading non trivial order in the gravitino and vector multiplet fermions. We find that both $R$-symmetry and flavor anomalies necessarily lead to a supersymmetry anomaly, thus generalizing our earlier results to non superconformal theories with Abelian flavor symmetries. The anomaly in the conservation of the supercurrent leads to an anomalous transformation for the supercurrent under rigid supersymmetry on bosonic backgrounds that admit new minimal Killing spinors. The resulting deformation of the supersymmetry algebra has implications for supersymmetric localization computations on such backgrounds.

34 pages; v2: generalized analysis of flavor supersymmetry anomalies; references added

References in corpus (13)

• Exploring 2-Group Global Symmetries
• On 2-Group Global Symmetries and Their Anomalies
• Localization on Hopf surfaces
• From Rigid Supersymmetry to Twisted Holomorphic Theories
• Holographic renormalization and supersymmetry
• Supersymmetric counterterms from new minimal supergravity
• Supersymmetry anomalies in $\mathcal{N}=1$ conformal supergravity
• Supersymmetric backgrounds from 5d N=1 supergravity
• Anomalous Supersymmetry
• Quantum consistency in supersymmetric theories with $R$-symmetry in curved space
• Supercurrent anomaly and gauge invariance in N=1 supersymmetric Yang-Mills theory
• Gravitational free energy in topological AdS/CFT
• Super-Weyl Anomaly from Holography and Rigid Supersymmetry Algebra on Two-Sphere

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• Conformal Contact Terms and Semi-Local Terms
• Supersymmetry anomaly in the superconformal Wess-Zumino model
• Consistency of supersymmetric 't Hooft anomalies
• Black hole superpotential as a unifying entropy function and BPS thermodynamics
• CP-violating supersymmetry anomaly
• Deformations of Supergravity and Supersymmetry Anomalies
• Anomalies and Supersymmetry
• Supersymmetry anomalies and the Wess-Zumino Model in a supergravity background