Anomaly-corrected supersymmetry algebra and supersymmetric holographic renormalization

Abstract

We present a systematic approach to supersymmetric holographic renormalization for a generic 5D $\mathcal{N}=2$ gauged supergravity theory with matter multiplets, including its fermionic sector, with all gauge fields consistently set to zero. We determine the complete set of supersymmetric local boundary counterterms, including the finite counterterms that parameterize the choice of supersymmetric renormalization scheme. This allows us to derive holographically the superconformal Ward identities of a 4D superconformal field theory on a generic background, including the Weyl and super-Weyl anomalies. Moreover, we show that these anomalies satisfy the Wess-Zumino consistency condition. The super-Weyl anomaly implies that the fermionic operators of the dual field theory, such as the supercurrent, do not transform as tensors under rigid supersymmetry on backgrounds that admit a conformal Killing spinor, and their anticommutator with the conserved supercharge contains anomalous terms. This property is explicitly checked for a toy model. Finally, using the anomalous transformation of the supercurrent, we obtain the anomaly-corrected supersymmetry algebra on curved backgrounds admitting a conformal Killing spinor.

arXiv comment51 pages; v2: two references added, typos corrected, a discussion about the 2-dimensional super-Weyl anomaly added in section 7

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• Supersymmetric Rényi entropy and charged hyperbolic black holes
• Supersymmetry anomalies in $\mathcal{N}=1$ conformal supergravity
• 't Hooft anomalies and the holomorphy of supersymmetric partition functions
• Anomalous Supersymmetry
• $\mathcal{N}=2$ AdS${}_4$ supergravity, holography and Ward identities
• Squashing the Boundary of Supersymmetric AdS${}_5$ Black Holes
• 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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• On the KKLT Goldstino
• Black hole superpotential as a unifying entropy function and BPS thermodynamics
• General Supersymmetric AdS${}_5$ Black Holes with Squashed Boundary
• Gravitational free energy in topological AdS/CFT
• Topological AdS/CFT and the $\Omega$ deformation
• CP-violating supersymmetry anomaly
• Super-Weyl Anomaly from Holography and Rigid Supersymmetry Algebra on Two-Sphere
• Anomalies and Supersymmetry
• Boundary Conditions in Topological AdS${}_4$/CFT${}_3$