Higher spins in AdS5_{5} at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT

Oct 13, 2014
57 pages
Published in:
  • JHEP 11 (2014) 114
  • Published: Nov 21, 2014
e-Print:
Report number:
  • IMPERIAL-TP-AT-2014-05

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Abstract: (Springer)
We consider general-symmetry higher spin fields in AdS5_{5} and derive the expressions for their one-loop corrections to vacuum energy Ec_{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 (Ec_{c} , 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_{c} , a, c) for the states at level p of Kaluza-Klein tower of 10d type IIB supergravity compactified on S5^{5} 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^{2} − 1 times that of one Maxwell multiplet). We also verify the matching of (Ec_{c} , 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_{5} containing fields in mixed-symmetry representations. We also discuss its supersymmetric generalizations.
Note:
  • 56 pages. v2,v3: minor corrections, references added
  • Higher Spin Symmetry
  • AdS-CFT Correspondence
  • Anomalies in Field and String Theories
  • field theory: conformal
  • spin: high
  • anomaly: conformal
  • vacuum state: energy
  • supergravity: conformal
  • supergravity: Type IIB
  • AdS/CFT correspondence