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arXiv · 1711.05530

Anomalous dimensions of spinning operators from conformal symmetry

Ferdinando Gliozzi
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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 $\ell=0,1,..$, 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 $ε\to 0$ 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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Ferdinando Gliozzi. 2017-11-27. Anomalous dimensions of spinning operators from conformal symmetry. https://doi.org/10.1007/jhep01(2018)113

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