M. Henningson and K. Skenderis JHEP07(1998)023 doi:10.1088/1126-6708/1998/07/023
The holographic Weyl anomaly
M. Henningson1 and K. Skenderis2
Show affiliationsWe 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 = 3l/2GN, in agreement with considerations based on the asymptotic symmetry algebra of adS3. In d = 4 the anomaly agrees precisely with that of the corresponding 
= 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.
- Keywords
- PACS
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11.25.Hf Conformal field theory, algebraic structures
11.15.Pg Expansions for large numbers of components (e.g., 1/Nc expansions)
- MSC
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81T13 Yang-Mills and other gauge theories (See also 53C07, 58E15)
81T40 Two-dimensional field theories, conformal field theories, etc.
81T30 String and superstring theories; other extended objects (e.g., branes) (See also 83E30)
- Subjects
- Dates
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Issue 07 ( 1 July 1998)
Received 17 June 1998, accepted for publication 30 July 1998
Published 23 September 1998
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