Abstract
We consider general-symmetry higher spin fields in AdS5 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 \( \mathcal{N}=8 \) gauged 5d supergravity are equal to \( -\frac{1}{2} \) of their values for \( \mathcal{N}=4 \) conformal 4d supergravity and also to twice the values for \( \mathcal{N}=4 \) Maxwell multiplet. This gives a 5d derivation of the fact that the system of \( \mathcal{N}=4 \) conformal supergravity and four \( \mathcal{N}=4 \) 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 \( \mathcal{N}=4 \) 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 \( \frac{1}{2} \) 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 AdS5 containing fields in mixed-symmetry representations. We also discuss its supersymmetric generalizations.
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Beccaria, M., Tseytlin, A.A. Higher spins in AdS5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT. J. High Energ. Phys. 2014, 114 (2014). https://doi.org/10.1007/JHEP11(2014)114
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DOI: https://doi.org/10.1007/JHEP11(2014)114