On harmonic measure of critical curves

Details On harmonic measure of critical curves On harmonic measure of critical curves

2005-07-12

arxiv.org/abs/hep-th/0507115v3

Phys.Rev.Lett.95:170602,2005

Physics

High Energy Physics

High Energy Physics - Theory

Some more corrections

Scientific paper

10.1103/PhysRevLett.95.170602

Fractal geometry of critical curves appearing in 2D critical systems is characterized by their harmonic measure. For systems described by conformal field theories with central charge $c\leqslant 1$, scaling exponents of harmonic measure have been computed by B. Duplantier [Phys. Rev. Lett. {\bf 84}, 1363 (2000)] by relating the problem to boundary two-dimensional gravity. We present a simple argument that allows us to connect harmonic measure of critical curves to operators obtained by fusion of primary fields, and compute characteristics of fractal geometry by means of regular methods of conformal field theory. The method is not limited to theories with $c\leqslant 1$.

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