# Anomaly-corrected supersymmetry algebra and supersymmetric holographic renormalization

## TL;DR

This paper develops a systematic method for supersymmetric holographic renormalization in 5D gauged supergravity, deriving superconformal Ward identities, anomalies, and an anomaly-corrected supersymmetry algebra for dual 4D superconformal field theories.

## Contribution

It introduces a comprehensive approach to supersymmetric holographic renormalization, including fermionic sectors and anomaly analysis, for 5D gauged supergravity with matter multiplets.

## Key findings

- Derived supersymmetric local boundary counterterms.
- Established superconformal Ward identities with anomalies.
- Obtained the anomaly-corrected supersymmetry algebra.

## Abstract

We present a systematic approach to supersymmetric holographic renormalization for a generic 5D $\mathcal{N}=2$ gauged supergravity theory with matter multiplets, including its fermionic sector, with all gauge fields consistently set to zero. We determine the complete set of supersymmetric local boundary counterterms, including the finite counterterms that parameterize the choice of supersymmetric renormalization scheme. This allows us to derive holographically the superconformal Ward identities of a 4D superconformal field theory on a generic background, including the Weyl and super-Weyl anomalies. Moreover, we show that these anomalies satisfy the Wess-Zumino consistency condition. The super-Weyl anomaly implies that the fermionic operators of the dual field theory, such as the supercurrent, do not transform as tensors under rigid supersymmetry on backgrounds that admit a conformal Killing spinor, and their anticommutator with the conserved supercharge contains anomalous terms. This property is explicitly checked for a toy model. Finally, using the anomalous transformation of the supercurrent, we obtain the anomaly-corrected supersymmetry algebra on curved backgrounds admitting a conformal Killing spinor.