ar X iv : h ep - t h / 03 04 23 8 v 1 2 8 A pr 2 00 3 The Holographic Supercurrent Anomaly

The γ-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 γ-trace anomaly of the supersymmetry current of N = 1 four-dimensional su-persymmetric gauge theory in a N = 1 conformal supergravity background can be extracted out from the 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 N = 2 bulk supersymmetry transformation converts into N = 1 superconformal transformation on the boundary, which consists of N = 1 supersymmetry transformation and special confor-mal supersymmetry (or super-Weyl) transformation; second the supersym-metry 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 field to the holographic superconformal anomaly is dominated by the leading terms in the asymptotic expansion of the bulk fields in terms of the radial coordinate, while external gravitational background contribution is determined by those terms with logarithmic function dependence on the radial coordinate.