A conformal bootstrap approach to critical percolation in two dimensions

Abstract

We study four-point functions of critical percolation in two dimensions, and more generally of the Potts model. We propose an exact ansatz for the spectrum: an infinite, discrete and non-diagonal combination of representations of the Virasoro algebra. Based on this ansatz, we compute four-point functions using a numerical conformal bootstrap approach. The results agree with Monte-Carlo computations of connectivities of random clusters.

16 pages, Python code available at https://github.com/ribault/bootstrap-2d-Python, v2: some clarifications and minor improvements

References in corpus (6)

• Logarithmic observables in critical percolation
• Conformal Fractal Geometry and Boundary Quantum Gravity
• Correlation functions in loop models
• Parafermionic excitations and critical exponents of random cluster and O(n) models
• Twist operator correlation functions in O(n) loop models
• Correlation function of four spins in the percolation model

Cited by in corpus (42)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$
• Integrability and Conformal Bootstrap: One Dimensional Defect CFT
• Geometrical four-point functions in the two-dimensional critical $Q$-state Potts model: The interchiral conformal bootstrap
• On four-point connectivities in the critical 2d Potts model
• Logarithmic CFT at generic central charge: from Liouville theory to the $Q$-state Potts model
• The analytic bootstrap equations of non-diagonal two-dimensional CFT
• Global symmetry and conformal bootstrap in the two-dimensional $O(n)$ model
• Conformal bootstrap for percolation and polymers
• The action of the Virasoro algebra in the two-dimensional Potts and loop models at generic $Q$
• Spaces of states of the two-dimensional O(n) and Potts models
• Exact logarithmic four-point functions in the critical two-dimensional Ising model
• Fusion in the periodic Temperley-Lieb algebra and connectivity operators of loop models
• Four-point geometrical correlation functions in the two-dimensional $Q$-state Potts model: connections with the RSOS models
• Four-point boundary connectivities in critical two-dimensional percolation from conformal invariance
• On 2d CFTs that interpolate between minimal models
• Two-point connectivity of two-dimensional critical $Q-$ Potts random clusters on the torus
• Integrability of Conformal Loop Ensemble: Imaginary DOZZ Formula and Beyond
• Conformally invariant boundary conditions in the antiferromagnetic Potts model and the $SL(2,\mathbb{R})/U(1)$ sigma model
• Particles, conformal invariance and criticality in pure and disordered systems
• The non-rational limit of D-series minimal models
• Schramm-Loewner evolution in 2d rigidity percolation
• Critical loop models are exactly solvable
• The action of the Virasoro algebra in quantum spin chains. I. The non-rational case
• Evidences of conformal invariance in 2d rigidity percolation
• Notes on the solutions of Zamolodchikov-type recursion relations in Virasoro minimal models
• Long-range quenched bond disorder in the bi-dimensional Potts model
• Topological effects and conformal invariance in long-range correlated random surfaces
• Three- and four-point connectivities of two-dimensional critical $Q-$ Potts random clusters on the torus
• 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
• Bootstrap approach to geometrical four-point functions in the two-dimensional critical $Q$-state Potts model: A study of the $s$-channel spectra
• Exact Correlation Functions in the Brownian Loop Soup
• Fusion rule in conformal field theories and topological orders: A unified view of correspondence and (fractional) supersymmetry and their relation to topological holography
• Crossing invariant correlation functions at $c=1$ from isomonodromic $\tau$ functions
• On the analytical continuation of lattice Liouville theory
• Crossing, Modular Averages and $N\leftrightarrow k$ in WZW Models
• Liouville quantum gravity weighted by conformal loop ensemble nesting statistics
• Logarithmic operators in $c=0$ bulk CFTs
• Analytic conformal bootstrap and Virasoro primary fields in the Ashkin-Teller model
• Fusion of spin fields in $W_3$ conformal field theories