The holographic Weyl anomaly

We calculate the Weyl anomaly for conformal field theories that can bedescribed via the adS/CFT correspondence. This entails regularizing thegravitational part of the corresponding supergravity action in a mannerconsistent with general covariance. Up to a constant, the anomaly only dependson the dimension d of the manifold on which the conformal field theory isdefined. We present concrete expressions for the anomaly in the physicallyrelevant cases d = 2, 4 and 6. In d = 2 we find for the central charge c = 3 l/2 G_N in agreement with considerations based on the asymptotic symmetry algebraof adS_3. In d = 4 the anomaly agrees precisely with that of the correspondingN = 4 superconformal SU(N) gauge theory. The result in d = 6 provides newinformation for the (0, 2) theory, since its Weyl anomaly has not been computedpreviously. The anomaly in this case grows as N^3, where N is the number ofcoincident M5 branes, and it vanishes for a Ricci-flat background.Comment: 12 pages, Latex, v2: minor improvement