Anomalous dimensions of higher spin currents in large N CFTs

A bstract We examine anomalous dimensions of higher spin currents in the critical O( N ) scalar model and the Gross-Neveu model in arbitrary d dimensions. These two models are proposed to be dual to the type A and type B Vasiliev theories, respectively. We reproduce the known results on the anomalous dimensions to the leading order in 1/ N by using conformal perturbation theory. This work can be regarded as an extension of previous work on the critical O( N ) scalars in 3 dimensions, where it was shown that the bulk computation for the masses of higher spin fields on AdS 4 can be mapped to the boundary one in conformal perturbation theory. The anomalous dimensions of the both theories agree with each other up to an overall factor depending only on d , and we discuss the coincidence for d = 3 by utilizing N = 2 supersymmetry.