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

Authors
  • Jacobsen, Jesper Lykke1, 2, 3
  • Saleur, Hubert3, 4
  • 1 PSL Research University, Laboratoire de Physique Théorique, Département de Physique de l’ENS, École Normale Supérieure, Sorbonne Université, CNRS, Paris, 75005, France , Paris (France)
  • 2 Sorbonne Université, École Normale Supérieure, CNRS, Laboratoire de Physique Théorique (LPT ENS), Paris, 75005, France , Paris (France)
  • 3 Institut de Physique Théorique, Université Paris Saclay, CEA, CNRS, Gif-sur-Yvette, 91191, France , Gif-sur-Yvette (France)
  • 4 University of Southern California, Department of Physics, Los Angeles, CA, 90089-0484, U.S.A. , Los Angeles (United States)
Type
Published Article
Journal
Journal of High Energy Physics
Publisher
Springer-Verlag
Publication Date
Jan 09, 2019
Volume
2019
Issue
1
Identifiers
DOI: 10.1007/JHEP01(2019)084
Source
Springer Nature
Keywords
License
Yellow

Abstract

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 hr,s where r is dense on the real axis.

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