Quantum consistency in supersymmetric theories with $R$-symmetry in curved space

Abstract

We discuss consistency at the quantum level in the rigid $\mathcal{N}=1$ supersymmetric field theories with a $U(1{)}_R$ symmetry in four-dimensional curved space which are formulated via coupling to the new-minimal supergravity background fields. By analyzing correlation functions of the current operators in the $\mathcal{R}$-multiplet, we show that the quantum consistency with the (unbroken) supersymmetry requires the $U(1{)}_R$ anomaly coefficient, which depends only on the field content of the theory, to vanish. This consistency condition is obtained under the assumption that the supercurrent Ward identity is non-anomalous and that the vacuum is supersymmetric.

arXiv comment15 pages plus 2 appendices, published version in JHEP, minor changes, references added

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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
• Deformations of Supergravity and Supersymmetry Anomalies
• Anomalies and Supersymmetry