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.

17 pages

References in corpus (5)

• Sphere Partition Functions and the Zamolodchikov Metric
• Localization on Hopf surfaces
• Holographic renormalization as a canonical transformation
• AdS${}_2$ Holographic Dictionary
• Holographic renormalization and supersymmetry

Cited by in corpus (1)

• Anomalous Supersymmetry