Abstract
We compute, to the first non-trivial order in the ϵ-expansion of a perturbed scalar field theory, the anomalous dimensions of an infinite class of primary operators with arbitrary spin ℓ = 0, 1, . . . , including as a particular case the weakly broken higher-spin currents, using only constraints from conformal symmetry. Following the bootstrap philosophy, no reference is made to any Lagrangian, equations of motion or coupling constants. Even the space dimensions d are left free. The interaction is implicitly turned on through the local operators by letting them acquire anomalous dimensions.
When matching certain four-point and five-point functions with the corresponding quantities of the free field theory in the ϵ → 0 limit, no free parameter remains. It turns out that only the expected discrete d values are permitted and the ensuing anomalous dimensions reproduce known results for the weakly broken higher-spin currents and provide new results for the other spinning operators.
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Gliozzi, F. Anomalous dimensions of spinning operators from conformal symmetry. J. High Energ. Phys. 2018, 113 (2018). https://doi.org/10.1007/JHEP01(2018)113
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DOI: https://doi.org/10.1007/JHEP01(2018)113