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

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 $r\in {\mathbb{N}}^{\ast }$, 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.

arXiv comment53 pages, 30 figures

References in corpus (30)

• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• Bounding scalar operator dimensions in 4D CFT
• Solving the 3D Ising Model with the Conformal Bootstrap
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Precision Islands in the Ising and $O(N)$ Models
• On the Liouville three-point function
• Dijet Cross Sections and Parton Densities in Diffractive DIS at HERA
• More constraining conformal bootstrap
• Critical exponents of the 3d Ising and related models from Conformal Bootstrap
• Liouville theory with a central charge less than one
• On three-point connectivity in two-dimensional percolation
• A conformal bootstrap approach to critical percolation in two dimensions
• Three-point functions in c <= 1 Liouville theory and conformal loop ensembles
• Connectivities of Potts Fortuin-Kasteleyn clusters and time-like Liouville correlator
• Logarithmic observables in critical percolation
• Potts q-color field theory and scaling random cluster model
• On four-point connectivities in the critical 2d Potts model
• Correlation functions in loop models
• Operator content of the critical Potts model in d dimensions and logarithmic correlations
• The analytic bootstrap equations of non-diagonal two-dimensional CFT
• Conformal bootstrap for percolation and polymers
• The periodic sl(2|1) alternating spin chain and its continuum limit as a bulk Logarithmic Conformal Field Theory at c=0
• 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
• Four-point geometrical correlation functions in the two-dimensional $Q$-state Potts model: connections with the RSOS models
• On 2d CFTs that interpolate between minimal models
• Four-point boundary connectivities in critical two-dimensional percolation from conformal invariance
• Two-point connectivity of two-dimensional critical $Q-$ Potts random clusters on the torus
• The non-rational limit of D-series minimal models
• Four spins correlation function of the $q$ states Potts model, for general values of $q$. Its percolation model limit $q\to 1$
• Three- and four-point connectivities of two-dimensional critical $Q-$ Potts random clusters on the torus

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• Reclaiming the Lost Conformality in a non-Hermitian Quantum 5-state Potts Model
• Integrability of Conformal Loop Ensemble: Imaginary DOZZ Formula and Beyond
• Particles, conformal invariance and criticality in pure and disordered systems
• Evidences of conformal invariance in 2d rigidity percolation
• The action of the Virasoro algebra in quantum spin chains. I. The non-rational case
• Critical loop models are exactly solvable
• Schramm-Loewner evolution in 2d rigidity percolation
• From combinatorial maps to correlation functions in loop models
• Low-temperature universal dynamics of the bidimensional Potts model in the large q limit
• Global symmetry and conformal bootstrap in the two-dimensional $Q$-state Potts model
• On the CFT describing the spin clusters in 2d Potts model
• Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds
• Boundary Criticality of Complex Conformal Field Theory: A Case Study in the Non-Hermitian 5-State Potts Model
• Liouville quantum gravity weighted by conformal loop ensemble nesting statistics
• Logarithmic operators in $c=0$ bulk CFTs
• On currents in the $O(n)$ loop model
• On the analytical continuation of lattice Liouville theory
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