Geometrical four-point functions in the two-dimensional critical Q-state Potts model: The interchiral conformal bootstrap

2020/05/14 by Yifei He, Jesper Lykke Jacobsen, Hubert Saleur · 1 citation
Physics and Astronomy · Mathematics · #hep-th #cond-mat.stat-mech #math-ph #math.MP

paper · pdf · doi:10.1007/jhep12(2020)019

53 pages, 30 figures

arxiv created 2020/05/14 · arxiv updated 2020/12/30

Abstract

Based on the spectrum identified in our earlier work [arXiv:1809.02191], we numerically solve the bootstrap to determine four-point correlation functions of the geometrical connectivities in the Q-state Potts model. Crucial in our approach is the existence of "interchiral conformal blocks", which arise from the degeneracy of fields with conformal weight h_r,1, with r∈ℕ^*, and are related to the underlying presence of the "interchiral algebra" introduced in [arXiv:1207.6334]. We also find evidence for the existence of "renormalized" recursions, replacing those that follow from the degeneracy of the field Φ₁₂^D in Liouville theory, and obtain the first few such recursions in closed form. This hints at the possibility of the full analytical determination of correlation functions in this model.

Citations

• Bootstrap approach to geometrical four-point functions in the two-dimensional critical Q-state Potts model: A study of the s-channel spectra
• Associative algebraic approach to logarithmic CFT in the bulk: the continuum limit of the gl(1|1) periodic spin chain, Howe duality and the interchiral algebra

Cited by

• The action of the Virasoro algebra in the two-dimensional Potts and loop models at generic Q