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 $1/N^2$. To order $1/N$ our results are in perfect agreement with those in the literature. To order $1/N^2$ we reproduce known results for anomalous dimensions and obtain a variety of new results for structure constants, including the global symmetry central charge $C_J$ to this order.

中文翻译：

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临界 O(N) 模型图表的替代方案：1/N2 阶的维度和结构常数

我们将现代分析引导程序的方法应用于 $1/N$ 扩展中的关键 $O(N)$ 模型。在无穷大 $N$ 时，模型具有更高的自旋对称性，当我们打开 $1/N$ 时，该对称性被弱破坏。通过研究四个基本场的相关器的一致性条件，我们推导出所有（断开的）电流的 CFT 数据订购 $1/N$，以及非单线电流的 CFT 数据订购 $1/N^2$ . 要订购 $1/N$，我们的结果与文献中的结果完全一致。为了订购 $1/N^2$，我们重现了异常维度的已知结果，并获得了结构常数的各种新结果，包括该订单的全局对称中心电荷 $C_J$。