  We consider conformal field theories with slightly broken higher spin
symmetry in arbitrary spacetime dimensions. We analyze the crossing equation in
the double light-cone limit and solve for the anomalous dimensions of higher
spin currents $\gamma_s$ with large spin $s$. The result depends on the
symmetries and the spectrum of the unperturbed conformal field theory. We
reproduce all known results and make further predictions. In particular we make
a prediction for the anomalous dimensions of higher spin currents in the 3d
Ising model.
