SLE-type growth processes and the Yang-Lee singularity

Details SLE-type growth processes and the Yang-Lee singularity SLE-type growth processes and the Yang-Lee singularity

2003-07-28

arxiv.org/abs/math-ph/0307058v3

J.Math.Phys. 45 (2004) 3040-3048

Physics

Mathematical Physics

12 pages, LaTeX, v2: thorough revision with corrections, v3: version to be published

Scientific paper

10.1063/1.1765747

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 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 to the Yang-Lee singularity. Our construction may thus offer a novel description of this statistical model.

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