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

Luis F. Alday; Johan Henriksson; Mark van Loon

doi:10.1007/jhep01(2020)063

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arXiv · 1907.02445

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

Luis F. Alday·Johan Henriksson·Mark van Loon

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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.

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Luis F. Alday, Johan Henriksson, Mark van Loon. 2019-07-04. An alternative to diagrams for the critical O(N) model: dimensions and structure constants to order $1/N^2$. https://doi.org/10.1007/jhep01(2020)063

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