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

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.

arXiv comment32 pages + appendices, 2 figures. v2: Improved presentation + new appendix considering mixed correlator. Version to appear in JHEP

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• Bootstrapping Monodromy Defects in the Wess-Zumino Model
• Vector model in various dimensions
• Perturbative and Nonperturbative Studies of CFTs with MN Global Symmetry
• Lightcone expansions of conformal blocks in closed form
• The background field method and critical vector models
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• More on Heavy-Light Bootstrap up to Double-Stress-Tensor
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• Casimir effect in critical $\mathrm{O}(N)$ models from non-equilibrium Monte Carlo simulations
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