### Abstract

Following S. Giombi and I. R. Klebanov, [J. High Energy Phys. 12 (2013) 068], we carry out one-loop tests of higher spin AdSd+1/CFTd correspondences for d≥2. The Vasiliev theories in AdSd+1, which contain each integer spin once, are related to the U(N) singlet sector of the d-dimensional CFT of N free complex scalar fields; the minimal theories containing each even spin once - to the O(N) singlet sector of the CFT of N free real scalar fields. Using analytic continuation of higher spin zeta functions, which naturally regulate the spin sums, we calculate one-loop vacuum energies in Euclidean AdSd+1. In even d we compare the result with the O(N0) correction to the a coefficient of the Weyl anomaly; in odd d - with the O(N0) correction to the free energy F on the d-dimensional sphere. For the theories of integer spins, the correction vanishes in agreement with the CFT of N free complex scalars. For the minimal theories, the correction always equals the contribution of one real conformal scalar field in d dimensions. As explained in Giombi and Klebanov, this result may agree with the O(N) singlet sector of the theory of N real scalar fields, provided the coupling constant in the higher spin theory is identified as GN∼1/(N-1). Our calculations in even d are closely related to finding the regularized a anomalies of conformal higher spin theories. In each even d we identify two such theories with vanishing a anomaly: a theory of all integer spins, and a theory of all even spins coupled to a complex conformal scalar. We also discuss an interacting UV fixed point in d=5 obtained from the free scalar theory via an irrelevant double-trace quartic interaction. This interacting large N theory is dual to the Vasiliev theory in AdS6 where the bulk scalar is quantized with the alternate boundary condition.

Original language | English (US) |
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Article number | 084004 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 89 |

Issue number | 8 |

DOIs | |

State | Published - Apr 1 2014 |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)

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## Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*89*(8), [084004]. https://doi.org/10.1103/PhysRevD.89.084004