Abstract
In a conformal field theory with weakly broken higher spin symmetry, the leading order anomalous dimensions of the broken currents can be efficiently determined from the structure of the classical non-conservation equations. We apply this method to the explicit example of O(N) invariant scalar field theories in various dimensions, including the large N critical O(N) model in general d, the Wilson-Fisher fixed point in d = 4 − ϵ, cubic scalar models in d = 6 − ϵ and the nonlinear sigma model in d = 2 + ϵ. Using information from the d = 4 − ϵ and d = 2 + ϵ expansions, we obtain some estimates for the dimensions of the higher spin operators in the critical 3d O(N) models for a few low values of N and spin.
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Giombi, S., Kirilin, V. Anomalous dimensions in CFT with weakly broken higher spin symmetry. J. High Energ. Phys. 2016, 68 (2016). https://doi.org/10.1007/JHEP11(2016)068
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DOI: https://doi.org/10.1007/JHEP11(2016)068