The holographic Weyl anomaly.

*(English)*Zbl 0958.81083Summary: We calculate the Weyl anomaly for conformal field theories that can be described via the AdS/CFT correspondence. This entails regularizing the gravitational part of the corresponding supergravity action in a manner consistent with general covariance. Up to a constant, the anomaly only depends on the dimension d of the manifold on which the conformal field theory is defined. We present concrete expressions for the anomaly in the physically relevant 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 algebra of \(\text{AdS}_3\). In \(d = 4\) the anomaly agrees precisely with that of the corresponding \(N = 4\) superconformal SU\((N)\) gauge theory. The result in \(d = 6\) provides new information for the \((0, 2)\) theory, since its Weyl anomaly has not been computed previously. The anomaly in this case grows as \(N^3\), where \(N\) is the number of coincident M5 branes, and it vanishes for a Ricci-flat background.