An alternative to diagrams for the critical O(N) model: dimensions and structure constants to order 1/N2

We apply the methods of modern analytic bootstrap to the critical O(N) model in a 1/N expansion. At infinite N the model possesses higher spin symmetry which is weakly broken as we turn on 1/N. By studying consistency conditions for the correlator of four fundamental fields we derive the CFT-data for all the (broken) currents to order 1/N, and the CFT-data for the non-singlet currents to order 1/N2. To order 1/N our results are in perfect agreement with those in the literature. To order 1/N2 we reproduce known results for anomalous dimensions and obtain a variety of new results for structure constants, including the global symmetry central charge CJ to this order