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Anomalous dimensions of higher spin currents in large \(N\) CFTs. (English) Zbl 1373.81326

Summary: 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 \( \mathcal{N}=2 \) supersymmetry.

MSC:

81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
83C25 Approximation procedures, weak fields in general relativity and gravitational theory
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