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

By Matteo Beccaria, A. Tseytlin. 2014

142 citations recorded by the source corpus.

A bstractWe consider general-symmetry higher spin fields in AdS5 and derive the expressions for their one-loop corrections to vacuum energy Ec 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 (Ec, a, c) computed for N=8$$ \mathcal{N}=8 $$ gauged 5d supergravity are equal to −12$$ -\frac{1}{2} $$ of their values for N=4$$ \mathcal{N}=4 $$ conformal 4d supergravity and also to twice the values for N=4$$ \mathcal{N}=4 $$ Maxwell multiplet. This gives a 5d derivation of the fact that the system of N=4$$ \mathcal{N}=4 $$ conformal supergravity and four N=4$$ \mathcal{N}=4 $$ Maxwell multiplets is anomaly free. The values of (Ec, a, c) for the states at level p of Kaluza-Klein tower of 10d type IIB supergravity compactified on S5 turn out to be equal to those for p copies of N=4$$ \mathcal{N}=4 $$ 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 N2 − 1 times that of one Maxwell multiplet). We also verify the matching of (Ec, a, c) for spin 0 and 12$$ \frac{1}{2} $$ 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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3538e1b3273e482dd5a838216d9e7db6853aa1a6

Citations in the corpus