The Holographic Supercurrent Anomaly

TL;DR

This paper explores how the b3-trace anomaly of the supersymmetry current in four-dimensional b1=1 supersymmetric gauge theories can be derived holographically from five-dimensional gauged supergravity, testing the AdS/CFT correspondence.

Contribution

It demonstrates the holographic derivation of the super-Weyl anomaly from b2=2 gauged supergravity and clarifies the role of supersymmetry transformations in this process.

Findings

Reproduction of the super-Weyl anomaly from five-dimensional supergravity.

The supersymmetry transformation in the bulk induces boundary superconformal transformations.

Supersymmetry variation of the bulk action is a total derivative, leading to the anomaly.

Abstract

The \gamma-trace anomaly of supersymmetry current in a supersymmetric gauge theory shares a superconformal anomaly multiplet with the chiral R-symmetry anomaly and the Weyl anomaly, and its holographic reproduction is a valuable test to the AdS/CFT correspondence conjecture. We investigate how the \gamma-trace anomaly of the supersymmetry current of {\cal N}=1 four-dimensional supersymmetric gauge theory in an {\cal N}=1 conformal supergravity background can be extracted out from the ${\cal N}=2$ gauged supergravity in five dimensions. It is shown that the reproduction of this super-Weyl anomaly originates from the following two facts: First the {\cal N}=2 bulk supersymmetry transformation converts into {\cal N}=1 superconformal transformation on the boundary, which consists of {\cal N}=1 supersymmetry transformation and special conformal supersymmetry (or super-Weyl) transformation; second the supersymmetry variation of the bulk action of five-dimensional gauged supergravity is a total derivative. The non-compatibility of supersymmetry and the super-Weyl transformation invariance yields the holographic supersymmetry current anomaly. Furthermore, we speculate on that the contribution from the external gauge and gravitational background fields to the superconformal anomaly may have different holographic origin.