2003/07/31 by Frédéric Lesage, Frederic Lesage, Jørgen Rasmussen +1 · 6 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Brownian motion #Conformal field theory #Conformal map #Field (mathematics) #Hierarchy #Null (SQL) #Null vector #Primary field #Random Matrices and Applications #Singularity #Stochastic processes and statistical mechanics #hep-th #math-ph #math.MP
paper · pdf · doi:10.1063/1.1765747
published in Journal of Mathematical Physics 45(8), 3040-3048 (American Institute of Physics) · 12 pages, LaTeX, v2: thorough revision with corrections, v3: version to be published
arxiv created 2004/04/29 · openalex publication_date 2004/06/24 · arxiv updated 2014/11/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The recently introduced SLE growth processes are based on conformal maps from an open and simply connected subset of the upper half-plane to the half-plane itself. We generalize this by considering a hierarchy of stochastic evolutions mapping open and simply connected subsets of smaller and smaller fractions of the upper half-plane to these fractions themselves. The evolutions are all driven by one-dimensional Brownian motion. Ordinary chordal SLE appears at grade one in the hierarchy. At grade two we find a direct correspondence to conformal field theory through the explicit construction of a level-four null vector in a highest-weight module of the Virasoro algebra. This conformal field theory has central charge c=−22/5 and is associated with the Yang–Lee singularity. Our construction may thus offer a novel description of this statistical model.