Gaussian free field and conformal field theory

Abstract

In these mostly expository lectures, we give an elementary introduction to conformal field theory in the context of probability theory and complex analysis. We consider statistical fields, and define Ward functionals in terms of their Lie derivatives. Based on this approach, we explain some equations of conformal field theory and outline their relation to SLE theory.

122 pages, 5 figures. To appear in Astérisque

References in corpus (5)

• Duality of Chordal SLE
• Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising model
• Critical percolation in the plane
• Multi-point Green's functions for SLE and an estimate of Beffara
• A contour line of the continuum Gaussian free field

Cited by in corpus (15)

• The random normal matrix model: insertion of a point charge
• A solution space for a system of null-state partial differential equations 3
• A non-Hermitian generalisation of the Marchenko-Pastur distribution: from the circular law to multi-criticality
• The high temperature crossover for general 2D Coulomb gases
• On boundary confinements for the Coulomb gas
• Conformal welding problem, flow line problem, and multiple Schramm--Loewner evolution
• Nesting statistics in the O(n) loop model on random planar maps
• Radial SLE martingale-observables
• QFT, RG, and all that, for mathematicians, in eleven pages
• Standard modules, radicals, and the valenced Temperley-Lieb algebra
• Conformal Field Theory, Vertex Operator Algebra and Stochastic Loewner Evolution in Ising Model
• Conformal field theory of dipolar SLE(4) with mixed boundary condition
• A massless quantum field theory over the p-adics
• Determinantal Point Processes, Stochastic Log-Gases, and Beyond
• Conformal field theory of dipolar SLE with the Dirichlet boundary condition