Anomalous dimensions of higher spin currents in large N CFTs

TL;DR

This paper calculates the anomalous dimensions of higher spin currents in large N conformal field theories, specifically the critical O(N) scalar and Gross-Neveu models, and compares results across different dimensions and dual theories.

Contribution

It extends previous work by computing anomalous dimensions in arbitrary dimensions and establishing their agreement between dual models using conformal perturbation theory.

Findings

Anomalous dimensions match between dual models up to a dimension-dependent factor.

Results reproduce known 3D cases and extend to arbitrary dimensions.

Agreement with bulk computations for higher spin masses in AdS.

Abstract

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.