The ABC (in any D) of Logarithmic CFT

Abstract

Logarithmic conformal field theories have a vast range of applications, from critical percolation to systems with quenched disorder. In this paper we thoroughly examine the structure of these theories based on their symmetry properties. Our analysis is model-independent and holds for any spacetime dimension. Our results include a determination of the general form of correlation functions and conformal block decompositions, clearing the path for future bootstrap applications. Several examples are discussed in detail, including logarithmic generalized free fields, holographic models, self-avoiding random walks and critical percolation.

55 pages + appendices

References in corpus (14)

• Massive Gravity in Three Dimensions
• Holographic c-theorems in arbitrary dimensions
• 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
• Critical Gravity in Four Dimensions
• Logarithmic extensions of minimal models: characters and modular transformations
• Associative-algebraic approach to logarithmic conformal field theories
• Critical exponents of the 3d Ising and related models from Conformal Bootstrap
• Kazhdan--Lusztig-dual quantum group for logarithmic extensions of Virasoro minimal models
• Ferromagnetic phase transition for the spanning-forest model (q \to 0 limit of the Potts model) in three or more dimensions
• Notes on instantons in topological field theory and beyond
• Consistent systems of correlators in non-semisimple conformal field theory
• W-Extended Logarithmic Minimal Models

Cited by in corpus (38)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• The critical O(N) CFT: Methods and conformal data
• Bi-scalar integrable CFT at any dimension
• On Higher-dimensional Carrollian and Galilean Conformal Field Theories
• Deligne Categories in Lattice Models and Quantum Field Theory, or Making Sense of $O(N)$ Symmetry with Non-integer $N$
• Generalized Fishnets and Exact Four-Point Correlators in Chiral CFT${}_4$
• Logarithmic CFT at generic central charge: from Liouville theory to the $Q$-state Potts model
• Bootstrapping hypercubic and hypertetrahedral theories in three dimensions
• Semi-classical BMS${}_3$ blocks and flat holography
• Loop-level gluon OPEs in celestial holography
• The renormalization group flow in field theories with quenched disorder
• Random Field Ising Model and Parisi-Sourlas Supersymmetry. Part II. Renormalization Group
• Conformal bootstrap for percolation and polymers
• On Galilean conformal bootstrap
• Conformal Bootstrap Analysis for Single and Branched Polymers
• The Shadow Formalism of Galilean CFT${}_2$
• A multicritical Landau-Potts field theory
• Critical gravity from four dimensional scale invariant gravity
• Four-point boundary connectivities in critical two-dimensional percolation from conformal invariance
• Bootstrapping Mixed MN Correlators in 3D
• Homoclinic RG flows, or when relevant operators become irrelevant
• Random Field ${\varphi }^3$ Model and Parisi-Sourlas Supersymmetry
• The tricritical Ising CFT and conformal bootstrap
• Combinatorial Solution of the Eclectic Spin Chain
• Operator mixing in massless QCD-like theories and Poincare'-Dulac theorem
• Supersymmetric Galilean conformal blocks
• Factorized lightcone expansion of conformal blocks
• Irrelevant and marginal deformed BMS field theories
• Hidden Conformal Symmetries from Killing Towers with an Application to Large-D/CFT
• Crossover exponents, fractal dimensions and logarithms in Landau-Potts field theories
• RG and logarithmic CFT multicritical properties of randomly diluted Ising models
• Logarithmic Vertex Algebras
• Spinors and conformal correlators
• Anomalous dimensions from conformal field theory: Generalized ${\varphi }^{2n+1}$ theories
• Accurate boundary bootstrap for the three-dimensional O($N$) normal universality class
• Logarithmic operators in $c=0$ bulk CFTs
• Analytic Bootstrap for Logarithmic CFT