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

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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.

A preprint version of the article is available at ArXiv.


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Correspondence to Johan Henriksson.

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ArXiv ePrint: 1907.02445

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Alday, L.F., Henriksson, J. & van Loon, M. An alternative to diagrams for the critical O(N) model: dimensions and structure constants to order 1/N2. J. High Energ. Phys. 2020, 63 (2020) doi:10.1007/JHEP01(2020)063

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  • Conformal Field Theory
  • Global Symmetries
  • 1/N Expansion