One loop tests of higher spin AdS/CFT
Abstract
Vasiliev's type A higher spin theories in AdS_{4} have been conjectured to be dual to the U( N) or O( N) singlet sectors in 3d conformal field theories with Ncomponent scalar fields. We compare the ( N ^{0}) correction to the 3sphere free energy F in the CFTs with corresponding calculations in the higher spin theories. This requires evaluating a regularized sum over one loop vacuum energies of an infinite set of massless higher spin gauge fields in Euclidean AdS_{4}. For the Vasiliev theory including fields of all integer spin and a scalar with ∆ = 1 boundary condition, we show that the regularized sum vanishes. This is in perfect agreement with the vanishing of subleading corrections to F in the U( N) singlet sector of the theory of N free complex scalar fields. For the minimal Vasiliev theory including fields of only even spin, the regularized sum remarkably equals the value of F for one free real scalar field. This result may agree with the O( N) singlet sector of the theory of N real scalar fields, provided the coupling constant in the Vasiliev theory is identified as G _{ N } ~ 1 /( N  1). Similarly, consideration of the USp( N) singlet sector for N complex scalar fields, which we conjecture to be dual to the husp(2; 0 4) Vasiliev theory, requires G _{ N } ~ 1 /( N + 1). We also test the higher spin AdS_{3} /CFT_{2} conjectures by calculating the regularized sum over one loop vacuum energies of higher spin fields in AdS_{3}. We match the esult with the ( N ^{0}) term in the central charge of the W _{ N } minimal models; this requires a certain truncation of the CFT operator spectrum so that the bulk theory contains two real scalar fields with the same boundary conditions.
 Publication:

Journal of High Energy Physics
 Pub Date:
 December 2013
 DOI:
 10.1007/JHEP12(2013)068
 arXiv:
 arXiv:1308.2337
 Bibcode:
 2013JHEP...12..068G
 Keywords:

 AdSCFT Correspondence;
 Models of Quantum Gravity;
 1/N Expansion;
 High Energy Physics  Theory
 EPrint:
 20 pages. v3: minor corrections, version published in JHEP