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23 April 2024

» arxiv » 2005.7258

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Geometrical four-point functions in the two-dimensional critical $Q$-state Potts model: The interchiral conformal bootstrap
Yifei He ; Jesper Lykke Jacobsen ; Hubert Saleur ;
Date:	14 May 2020
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 $rinmathbb{N}^*$, 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 $Phi_{12}^D$ 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.
Source:	arXiv, 2005.7258
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