Super-Weyl anomaly from holography and rigid supersymmetry algebra on a two-sphere

Operators transform anomalously under the symmetry in the presence of quantum anomalies. We study this aspect of the super-Weyl anomaly in N=(1,1) superconformal field theories (SCFTs), in the context of AdS/CFT. In particular, we carry out holographic renormalization for (1,1) pure AdS₃ supergravity that is supposed to be a gravity dual of the N=(1,1) SCFT, and derive holographic superconformal Ward identities with corresponding anomalies. We show that the obtained super-Weyl anomaly of the 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 N=(1,1) rigid supersymmetry algebra on a two-sphere.