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Operators transform anomalously under the symmetry in the presence of quantumanomalies. We study this aspect of the super-Weyl anomaly in $\mathcal N=(1,1)$superconformal field theories (SCFTs), in the context of AdS/CFT. Inparticular, 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 correspondinganomalies. We show that the obtained super-Weyl anomaly of the $\mathcalN=(1,1)$ SCFT induces a quantum correction term in the transformation law ofthe supercurrent under the rigid supersymmetry. We demonstrate that thecorrection term does not affect the $\mathcal N=(1,1)$ rigid supersymmetryalgebra on two-sphere.

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