Conformal bootstrap for percolation and polymers

Abstract

The conformal bootstrap is applied to percolation and dilute self-avoiding polymers, two theories with Virasoro central charge $c=0$ in two dimensions. In both cases we propose a spectrum of operators motivated by Virasoro symmetry which is devoid of a stress energy tensor as an approximate means of enforcing $c=0$. Percolation is treated in $2\le D\le 6$ dimensions, and the self-avoiding walk in $2\le D\le 4$.

25 pages, 10 figures. v3: published version

References in corpus (16)

• Anderson Transitions
• 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
• Bootstrapping Mixed Correlators in the 3D Ising Model
• Large Spin Perturbation Theory
• Conformal Bootstrap in Mellin Space
• Bounds in 4D Conformal Field Theories with Global Symmetry
• Central Charge Bounds in 4D Conformal Field Theory
• Critical exponents of the 3d Ising and related models from Conformal Bootstrap
• Closure of the Operator Product Expansion in the Non-Unitary Bootstrap
• A conformal bootstrap approach to critical percolation in two dimensions
• The ABC (in any D) of Logarithmic CFT
• JuliBootS: a hands-on guide to the conformal bootstrap
• Parafermionic excitations and critical exponents of random cluster and O(n) models
• New method for the conformal bootstrap with OPE truncations
• Correlation function of four spins in the percolation model

Cited by in corpus (17)

• Five loop renormalization of ${\varphi }^3$ theory with applications to the Lee-Yang edge singularity and percolation theory
• The extraordinary boundary transition in the 3d O(N) model via conformal bootstrap
• Geometrical four-point functions in the two-dimensional critical $Q$-state Potts model: The interchiral conformal bootstrap
• Rigorous bounds on irrelevant operators in the 3d Ising model CFT
• On four-point connectivities in the critical 2d Potts model
• Solving Conformal Field Theories with Artificial Intelligence
• Geometric properties of the Fortuin-Kasteleyn representation of the Ising model
• Improving the five-point bootstrap
• Ising model close to $d=2$
• Two-point connectivity of two-dimensional critical $Q-$ Potts random clusters on the torus
• Critical exponents and universal excess cluster number of percolation in four and five dimensions
• Observation of non-scalar and logarithmic correlations in 2D and 3D percolation
• Easy bootstrap for the 3D Ising model: a hybrid approach of the lightcone bootstrap and error minimization methods
• Factorized lightcone expansion of conformal blocks
• Extrapolation from hypergeometric functions, continued functions and Borel-Leroy transformation; Resummation of perturbative renormalization functions from field theories
• Conformal Bootstrap with Reinforcement Learning
• Accurate boundary bootstrap for the three-dimensional O($N$) normal universality class