Bootstrap approach to geometrical four-point functions in the two-dimensional critical $Q$-state Potts model: A study of the $s$-channel spectra - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of High Energy Physics Année : 2019

Bootstrap approach to geometrical four-point functions in the two-dimensional critical $Q$-state Potts model: A study of the $s$-channel spectra

Résumé

We revisit in this paper the problem of connectivity correlations in the Fortuin-Kasteleyn cluster representation of the two-dimensional Q-state Potts model conformal field theory. In a recent work [1], results for the four-point functions were obtained, based on the bootstrap approach, combined with simple conjectures for the spectra in the different fusion channels. In this paper, we test these conjectures using lattice algebraic considerations combined with extensive numerical studies of correlations on infinite cylinders. We find that the spectra in the scaling limit are much richer than those proposed in [1]: they involve in particular fields with conformal weight h$_{r,s}$ where $r$ is dense on the real axis.
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Dates et versions

hal-01897182 , version 1 (20-04-2023)

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Jesper Lykke Jacobsen, Hubert Saleur. Bootstrap approach to geometrical four-point functions in the two-dimensional critical $Q$-state Potts model: A study of the $s$-channel spectra. Journal of High Energy Physics, 2019, 2019, pp.084. ⟨10.1007/JHEP01(2019)084⟩. ⟨hal-01897182⟩
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