Higher spins in AdS5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT

We consider general-symmetry higher spin fields in AdS(5) and derive the expressions for their one-loop corrections to vacuum energy E-c and the associated 4d boundary conformal anomaly a-coefficient. We propose a similar expression for the second conformal anomaly c-coefficient. We show that all the three quantities (E-c, a, c) computed for N = 8 gauged 5d supergravity are equal to -1/2 of their values for N = 4 conformal 4d supergravity and also to twice the values for N = 4 Maxwell multiplet. This gives a 5d derivation of the fact that the system of N = 4 conformal supergravity and four N = 4 Maxwell multiplets is anomaly free. The values of (E-c, a, c) for the states at level p of Kaluza-Klein tower of 10d type IIB supergravity compactified on S-5 turn out to be equal to those for p copies of N = 4 Maxwell multiplets. This may be related to the fact that these states appear in the tensor product of p superdoubletons. Under a natural regularization of the sum over p, the full 10d supergravity contribution is then minus that of one Maxwell multiplet, in agreement with the standard adjoint AdS/CFT duality (SU(N) SYM contribution is N-2 - 1 times that of one Maxwell multiplet). We also verify the matching of (E-c, a, c) for spin 0 and 1/2 boundary theory cases of vectorial AdS/CFT duality. The consistency conditions for vectorial AdS/CFT turn out to be equivalent to the cancellation of anomalies in the closely related 4d conformal higher spin theories. In addition, we study novel example of the vectorial AdS/CFT duality when the boundary theory is described by free spin 1 fields and is dual to a particular higher spin theory in AdS(5) containing fields in mixed-symmetry representations. We also discuss its supersymmetric generalizations.