Super-Weyl Anomaly from Holography and Rigid Supersymmetry Algebra on Two-Sphere

Abstract

Operators transform anomalously under the symmetry in the presence of quantum anomalies. We study this aspect of the super-Weyl anomaly in $\mathcal{N}=(1,1)$ superconformal field theories (SCFTs), in the context of AdS/CFT. In particular, we carry out holographic renormalization for $(1,1)$ pure AdS${}_3$ supergravity that is supposed to be a gravity dual of the $\mathcal{N}=(1,1)$ SCFT, and derive holographic superconformal Ward identities with corresponding anomalies. We show that the obtained super-Weyl anomaly of the $\mathcal{N}=(1,1)$ SCFT induces a quantum correction term in the transformation law of the supercurrent under the rigid supersymmetry. We demonstrate that the correction term does not affect the $\mathcal{N}=(1,1)$ rigid supersymmetry algebra on two-sphere.

arXiv comment17 pages

References in corpus (23)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• The Holographic Weyl anomaly
• Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• Partition functions of N=(2,2) gauge theories on S^2 and vortices
• A Construction of Killing Spinors on S^n
• The Geometry of Supersymmetric Partition Functions
• Sphere Partition Functions and the Zamolodchikov Metric
• Localization on Hopf surfaces
• Holographic Renormalization of general dilaton-axion gravity
• Holographic Renormalization and Ward Identities with the Hamilton-Jacobi Method
• Holographic renormalization as a canonical transformation
• AdS${}_2$ Holographic Dictionary
• On the origin of supergravity boundary terms in the AdS/CFT correspondence
• Holographic renormalization and supersymmetry
• Supercurrent anomalies in 4d SCFTs
• Boundary Terms and Three-Point Functions: An AdS/CFT Puzzle Resolved
• The gravity dual of supersymmetric gauge theories on a squashed $S^1\times S^3$
• Anomaly-corrected supersymmetry algebra and supersymmetric holographic renormalization
• The holographic supersymmetric Casimir energy
• Super Weyl Anomalies in the AdS/CFT Correspondence
• Holographic Renormalization Group with Fermions and Form Fields

Cited by in corpus (3)

• Anomalous Supersymmetry
• Supersymmetry anomalies in new minimal supergravity
• Supersymmetry anomaly in the superconformal Wess-Zumino model