THE HOLOGRAPHIC WEYL ANOMALY

We calculate the Weyl anomaly for conformal field theories that can be described via the adS/CFT correspondence. This entails regularizing t he gravitational part of the corresponding supergravity action in a ma nner consistent with general covariance. Up to a constant, the anomaly only depends on the dimension d of the manifold on which the conforma l field theory is defined. We present concrete expressions for the ano maly in the physically relevant cases d = 2, 4 and 6. In d = 2 we find for the central charge c = 3l/2G(N), in agreement with considerations based on the asymptotic symmetry algebra of adS(3). In d = 4 the anom aly agrees precisely with that of the corresponding N = 4 superconform al SU(N) gauge theory. The result in d = 6 provides new information fo r the (0; 2) theory, since its Weyl anomaly has not been computed prev iously. The anomaly in this case grows as N-3, where N is the number o f coincident M5 branes, and it vanishes for a Ricci-flat background.