Geometrical four-point functions in the two-dimensional critical $Q$-state Potts model: The interchiral conformal bootstrap
| Autor: | Yifei He, Jesper Lykke Jacobsen, Hubert Saleur |
|---|---|
| Přispěvatelé: | Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), University of California [Los Angeles] (UCLA), University of California (UC), European Project: 669205,H2020,ERC-2014-ADG,NuQFT(2015) |
| Rok vydání: | 2020 |
| Předmět: |
High Energy Physics - Theory
Nuclear and High Energy Physics Pure mathematics geometry bootstrap: conformal conformal block Lattice Integrable Models [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] FOS: Physical sciences Field (mathematics) Conformal map 01 natural sciences 0103 physical sciences Potts model lcsh:Nuclear and particle physics. Atomic energy. Radioactivity Point (geometry) correlation function numerical calculations dimension: 2 010306 general physics Condensed Matter - Statistical Mechanics Mathematical Physics Physics Conformal Field Theory Statistical Mechanics (cond-mat.stat-mech) [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] Field Theories in Lower Dimensions 010308 nuclear & particles physics Conformal field theory Spectrum (functional analysis) State (functional analysis) Mathematical Physics (math-ph) [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph] field theory: Liouville High Energy Physics - Theory (hep-th) lcsh:QC770-798 n-point function: 4 Degeneracy (mathematics) |
| Zdroj: | Journal of High Energy Physics, Vol 2020, Iss 12, Pp 1-60 (2020) Journal of High Energy Physics Journal of High Energy Physics, Springer, 2020, 12, pp.019. ⟨10.1007/JHEP12(2020)019⟩ Journal of High Energy Physics, 2020, 2020 (12), pp.019. ⟨10.1007/JHEP12(2020)019⟩ JHEP |
| ISSN: | 1126-6708 1029-8479 |
| DOI: | 10.48550/arxiv.2005.07258 |
| Popis: | 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 $r\in\mathbb{N}^*$, 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. Comment: 53 pages, 30 figures |
| Databáze: | OpenAIRE |
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