Higher spin AdSd_{+1}/CFT_{d} at one loop
Abstract
Following S. Giombi and I. R. Klebanov, [J. High Energy Phys. 12 (2013) 068], we carry out oneloop tests of higher spin AdS_{d +1}/CFT_{d} 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 ddimensional 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 oneloop vacuum energies in Euclidean AdSd_{+1}. In even d we compare the result with the O(N^{0}) correction to the a coefficient of the Weyl anomaly; in odd d—with the O(N^{0}) correction to the free energy F on the ddimensional 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 G_{N}∼1/(N1). 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 doubletrace quartic interaction. This interacting large N theory is dual to the Vasiliev theory in AdS_{6} where the bulk scalar is quantized with the alternate boundary condition.
 Publication:

Physical Review D
 Pub Date:
 April 2014
 DOI:
 10.1103/PhysRevD.89.084004
 arXiv:
 arXiv:1401.0825
 Bibcode:
 2014PhRvD..89h4004G
 Keywords:

 04.50.h;
 04.62.+v;
 11.25.Tq;
 Higherdimensional gravity and other theories of gravity;
 Quantum field theory in curved spacetime;
 Gauge/string duality;
 High Energy Physics  Theory
 EPrint:
 35 pages. v2: minor improvements