Anomalous dimensions of spinning operators from conformal symmetry

We compute, to the first non-trivial order in the epsilon-expansion of a perturbed scalar field theory, the anomalous dimensions of an in finite 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 dare 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 epsilon -> 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.