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.

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

References in corpus (7)

• Holographic renormalization as a canonical transformation
• A supersymmetric consistent truncation for conifold solutions
• Holographic renormalization and supersymmetry
• Supersymmetric Consistent Truncations of IIB on T(1,1)
• Supercurrent anomalies in 4d SCFTs
• Supergravity at the boundary of AdS supergravity
• The Holographic Goldstino

Cited by in corpus (25)

• Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS${}_5$ black holes
• The BPS limit of rotating AdS black hole thermodynamics
• A gravity interpretation for the Bethe Ansatz expansion of the $\mathcal{N}=4$ SYM index
• A note on the entropy of rotating BPS AdS${}_7\times S^4$ black holes
• The large-$N$ limit of the 4d $\mathcal{N}=1$ superconformal index
• Entropy functional and the holographic attractor mechanism
• 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
• Quantum consistency in supersymmetric theories with $R$-symmetry in curved space
• 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${}_3$