Supersymmetry anomalies in $\mathcal{N}=1$ conformal supergravity

Abstract

We solve the Wess-Zumino consistency conditions of $\mathcal{N}=1$ off-shell conformal supergravity in four dimensions and determine the general form of the superconformal anomalies for arbitrary $a$ and $c$ anomaly coefficients to leading non trivial order in the gravitino. Besides the well known Weyl and $R$-symmetry anomalies, we compute explicitly the fermionic $\mathcal{Q}$- and $\mathcal{S}$-supersymmetry anomalies. In particular, we show that $\mathcal{Q}$-supersymmetry is anomalous if and only if $R$-symmetry is anomalous. The $\mathcal{Q}$- and $\mathcal{S}$-supersymmetry anomalies give rise to an anomalous supersymmetry transformation for the supercurrent on curved backgrounds admitting Killing spinors, resulting in a deformed rigid supersymmetry algebra. Our results may have implications for supersymmetric localization and supersymmetry phenomenology. Analogous results are expected to hold in dimensions two and six and for other supergravity theories. The present analysis of the Wess-Zumino consistency conditions reproduces the holographic result of arxiv:1703.04299 and generalizes it to arbitrary $a$ and $c$ anomaly coefficients.

arXiv comment13+13 pages; v2: minor corrections and improvements; references added; v3: further minor typos corrected; version published in JHEP

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• Anomalous Supersymmetry
• $\mathcal{N}=2$ AdS${}_4$ supergravity, holography and Ward identities
• Comments on Anomalies in Supersymmetric Theories
• Supersymmetry anomalies in new minimal supergravity
• Conformal Contact Terms and Semi-Local Terms
• Supersymmetry anomaly in the superconformal Wess-Zumino model
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• Consistency of supersymmetric 't Hooft anomalies
• Black hole superpotential as a unifying entropy function and BPS thermodynamics
• Superconformal anomalies from superconformal Chern-Simons polynomials
• Topological AdS/CFT and the $\Omega$ deformation
• CP-violating supersymmetry anomaly
• Anomalies and Supersymmetry
• Supersymmetry anomalies and the Wess-Zumino Model in a supergravity background