Higher spins in AdS_5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT

We consider general-symmetry higher spin fields in AdS_5 and derive expressions for their one-loop corrections to vacuum energy E and the associated 4d boundary conformal anomaly a-coefficient. We a propose a similar expression for the second conformal anomaly c-coefficient. We show that all the three quantities (E, a, c) computed for N=8 gauged 5d supergravity are -1/2 of the values for N=4 conformal 4d supergravity and also twice the values for N=4 Maxwell multiplet. This gives 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, 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 the Maxwell multiplet, in agreement with the standard adjoint AdS/CFT duality (SU(n) SYM contribution is n^2-1 of one Maxwell multiplet). We also verify the matching of (E, 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 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.