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Universal central charge in higher dimensional AdS/CFT?

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In the $AdS_3/CFT_2$ correspondence, the central charge of the dual CFT2 is universally given by $$ c = \frac{3\ell}{2G} $$ This is independent of the matter in the bulk of AdS3. Is it also universal in the higher dimensional analogues $AdS_d/CFT_{d-1}$ or does it depend on details of the matter in the bulk, etc.?

In particular, what is the central charge for $d=4$?

This post imported from StackExchange Physics at 2014-06-11 20:44 (UCT), posted by SE-user Prahar

asked Jun 10, 2014 in Theoretical Physics by prahar21 (545 points) [ no revision ]

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