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We propose a general method for the numerical evaluation of OPE coefficients in three dimensional Conformal Field Theories based on the study of the conformal perturbation of two point functions in the vicinity of the critical point.
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As far as we know the only other existing estimate for this constant was obtained by Henkel [ 31 ] in the Hamiltonian limit. A puzzling feature of his result is that, in disagreement with our finding and with [ 19 ] he found different values for C σ σ ϵ C_{\sigma\sigma}^{\epsilon} and C σ ϵ σ C_{\sigma\epsilon}^{\sigma} . While his value for C σ ϵ σ C_{\sigma\epsilon}^{\sigma} agrees within the errors with our result, C σ σ ϵ C_{\sigma\sigma}^{\epsilon} is incompatible. As noticed in [ 19 ] , this is most probably due to the fact that the Hamiltonian setting of Henkel’s calculation is not Weyl equivalent to the flat 3d space in which both our simulations and the bootstrap calculations are performed.
Cited in the paper.
S. El-Showk, M. Paulos, D. Poland, S. Rychkov, D. Simmons-Duffin and A. Vichi, Phys. Rev. Lett. 112
2014
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F. Kos, D. Poland and D. Simmons-Duffin, JHEP 1411
2014
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S. El-Showk, M. F. Paulos, D. Poland, S. Rychkov, D. Simmons-Duffin and A. Vichi, J. Stat. Phys. 157
2014
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D. Gaiotto, D. Mazac and M. F. Paulos, JHEP 1403
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D. Poland and D. Simmons-Duffin, JHEP 1105
2087
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