The Holographic Weyl anomaly

1998/06/17 by Mans Henningson, Kostas Skenderis · 6 citations
Physics and Astronomy · #hep-th

paper · pdf · doi:10.1088/1126-6708/1998/07/023

published as JHEP 9807 (1998) 023 · 12 pages, Latex, v2: minor improvements

arxiv created 1998/06/17 · arxiv updated 2009/11/30

Abstract

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 adS₃. 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 N³, where N is the number of coincident M5 branes, and it vanishes for a Ricci-flat background.

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