### On partition function and Weyl anomaly of conformal higher spin fields,” arXiv:1309.0785 [hep-th

"... iv ..."

### Higher symmetries of the conformal powers of the Laplacian on conformally at manifolds

- J. Math. Phys

"... ar ..."

(Show Context)
### Determinant and Weyl anomaly of Dirac operator: a holographic derivation,” J.Phys. A45

, 2012

"... ar ..."

(Show Context)
### Imperial-TP-AT-2013-6 Weyl anomaly of conformal higher spins on six-sphere

"... ar ..."

(Show Context)
### A Note on Scalar Field Theory in AdS3/CFT2

, 902

"... We consider a scalar field theory in AdSd+1, and introduce a formalism on surfaces at equal values of the radial coordinate. In particular, we define the corresponding conjugate momentum. We compute the Noether currents for isometries in the bulk, and carefully perform the asymptotic limit on the co ..."

Abstract
- Add to MetaCart

We consider a scalar field theory in AdSd+1, and introduce a formalism on surfaces at equal values of the radial coordinate. In particular, we define the corresponding conjugate momentum. We compute the Noether currents for isometries in the bulk, and carefully perform the asymptotic limit on the corresponding ‘conserved ’ charges. We then introduce Poisson brackets at the border, and show that the asymptotic values of the bulk scalar field and the conjugate momentum transform as conformal fields of scaling dimensions ∆ − and ∆+, respectively, where ∆ ± are the standard parameters giving the asymptotic behavior of the scalar field in AdS. Then we consider the case d = 2, where the boundary is described in terms of complex holomorphic and antiholomorphic coordinates. We obtain two copies of the Virasoro algebra, with vanishing central charge. An AdS3/CFT2 prescription, giving the commutators of the boundary CFT in terms of the Poisson brackets at the border, arises in a natural way. We find that the boundary CFT is similar to a generalized ghost system. We introduce

### A Note on Scalar Field Theory in AdS3/CFT2

, 902

"... We consider a scalar field theory in AdSd+1, and introduce a formalism on surfaces at equal values of the radial coordinate. In particular, we define the corresponding conjugate momentum. We compute the Noether currents for isometries in the bulk, and carefully perform the asymptotic limit on the co ..."

Abstract
- Add to MetaCart

We consider a scalar field theory in AdSd+1, and introduce a formalism on surfaces at equal values of the radial coordinate. In particular, we define the corresponding conjugate momentum. We compute the Noether currents for isometries in the bulk, and carefully perform the asymptotic limit on the corresponding ‘conserved ’ charges. We then introduce Poisson brackets at the border, and show that the asymptotic values of the bulk scalar field and the conjugate momentum transform as conformal fields of scaling dimensions ∆ − and ∆+, respectively, where ∆ ± are the standard parameters giving the asymptotic behavior of the scalar field in AdS. Then we consider the case d = 2, where the boundary is described in terms of complex holomorphic and antiholomorphic coordinates. We obtain two copies of the Virasoro algebra, with vanishing central charge. An AdS3/CFT2 prescription, giving the commutators of the boundary CFT in terms of the Poisson brackets at the border, arises in a natural way. We find that the boundary CFT is similar to a generalized ghost system. We introduce

### Imperial-TP-AT-2014-05 Higher spins in AdS5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT

"... Abstract: We consider general-symmetry higher spin fields in AdS5 and derive the ex-pressions 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 tha ..."

Abstract
- Add to MetaCart

(Show Context)
Abstract: We consider general-symmetry higher spin fields in AdS5 and derive the ex-pressions 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 gauged 5d supergravity are equal to −12 of their values for N = 4 conformal 4d supergravity and also to twice the values for N = 4 Maxwell multiplet. This gives a 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 (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 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 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.