# An alternative to diagrams for the critical O(N) model: dimensions and structure constants to order $1/N^2$

## TL;DR

This paper uses modern analytic bootstrap methods to compute the critical O(N) model's dimensions and structure constants up to order 1/N^2, providing new insights into its symmetry breaking and CFT data.

## Contribution

It extends previous results by calculating structure constants and CFT data at order 1/N^2, including the global symmetry central charge, using analytic bootstrap techniques.

## Key findings

- Agreement with known 1/N results
- New structure constants at order 1/N^2
- Computed the global symmetry central charge C_J

## Abstract

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.