Correlation functions in loop models

Abstract

In this paper we provide a step towards the understanding of the O($n$) bulk operator algebra. By using a mixture of analytical and numerical methods, we compute (ratios of) structure constants, and analyse the logarithmic structure of the transfer matrix. We believe that the O($n$) model for a generic value of $n=q+q^{-1}$ (i.e. for $q$ not a root of unity) provides a toy model of a bulk logarithmic CFT that is considerably simpler than its counterparts at $q$ a root of unity.

36 pages + appendix, 7 figures

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Cited by in corpus (18)

• A conformal bootstrap approach to critical percolation in two dimensions
• Three-point functions in c <= 1 Liouville theory and conformal loop ensembles
• Geometrical four-point functions in the two-dimensional critical $Q$-state Potts model: The interchiral conformal bootstrap
• On four-point connectivities in the critical 2d Potts model
• Global symmetry and conformal bootstrap in the two-dimensional $O(n)$ model
• Fusion in the periodic Temperley-Lieb algebra and connectivity operators of loop models
• Two-point connectivity of two-dimensional critical $Q-$ Potts random clusters on the torus
• The fully packed loop model as a non-rational $W_3$ conformal field theory
• Critical loop models are exactly solvable
• Long-range quenched bond disorder in the bi-dimensional Potts model
• Three- and four-point connectivities of two-dimensional critical $Q-$ Potts random clusters on the torus
• Global symmetry and conformal bootstrap in the two-dimensional $Q$-state Potts model
• Bootstrap approach to geometrical four-point functions in the two-dimensional critical $Q$-state Potts model: A study of the $s$-channel spectra
• Level Set Percolation in Two-Dimensional Gaussian Free Field
• The imaginary Toda field theory
• Logarithmic operators in $c=0$ bulk CFTs
• Conformal amplitude hierarchy and the Poincare disk
• Analytic conformal bootstrap and Virasoro primary fields in the Ashkin-Teller model