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

## TL;DR

This paper investigates the super-Weyl anomaly in =(1,1) superconformal field theories using holography, deriving Ward identities and showing the anomaly's effect on supercurrent transformations without altering the supersymmetry algebra.

## Contribution

It provides a holographic derivation of the super-Weyl anomaly and analyzes its impact on the supersymmetry algebra in =(1,1) SCFTs on a two-sphere.

## Key findings

- Holographic superconformal Ward identities with anomalies derived.
- Super-Weyl anomaly induces quantum corrections in supercurrent transformations.
- The anomaly does not modify the =(1,1) supersymmetry algebra on the 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.