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

• Published in: The journal of high energy physics Vol. 2020; no. 12; pp. 1 - 60
• Main Authors: He, Yifei, Jacobsen, Jesper Lykke, Saleur, Hubert
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2020; Springer Nature B.V; Springer; SpringerOpen
• Subjects: Classical and Quantum Gravitation; Conformal Field Theory; Correlation analysis; Elementary Particles; Field Theories in Lower Dimensions; Field theory; General Physics; High energy physics; High Energy Physics - Theory; Lattice Integrable Models; Mathematical analysis; Mathematical Physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Two dimensional models; Field Theories in Lower Dimensions; Lattice Integrable Models; Conformal Field Theory; n-point function: 4; numerical calculations; dimension: 2; bootstrap: conformal; geometry; Potts model; field theory: Liouville; conformal block; correlation function
• ISSN: 1029-8479; 1126-6708; 1029-8479
• DOI: 10.1007/JHEP12(2020)019

A bstract Based on the spectrum identified in our earlier work [ 1 ], 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 [ 2 ]. We also find evidence for the existence of “renormalized” recursions, replacing those that follow from the degeneracy of the field Φ 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.