Higher spins in AdS at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT
Oct 13, 201457 pages
Published in:
- JHEP 11 (2014) 114
- Published: Nov 21, 2014
e-Print:
- 1410.3273 [hep-th]
Report number:
- IMPERIAL-TP-AT-2014-05
View in:
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Abstract: (Springer)
We consider general-symmetry higher spin fields in AdS and derive the expressions for their one-loop corrections to vacuum energy E 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 , a, c) computed for gauged 5d supergravity are equal to of their values for conformal 4d supergravity and also to twice the values for Maxwell multiplet. This gives a 5d derivation of the fact that the system of conformal supergravity and four 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 turn out to be equal to those for p copies of 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 − 1 times that of one Maxwell multiplet). We also verify the matching of (E , a, c) for spin 0 and 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 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
References(136)
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