English

Conformal fields, restriction properties, degenerate representations and SLE

Probability 2007-05-23 v2 Mathematical Physics math.MP Representation Theory

Abstract

In this note, we show how to relate the Schramm-Loewner Evolution processes (SLE) to highest-weight representations of the Virasoro Algebra. The conformal restriction properties of SLE that have been recently studied in the paper arXiv:math.PR/0209343 by G. Lawler, O. Schramm and the second author play an instrumental role. In this setup, various considerations from conformal field theory can be interpreted and reformulated via SLE. This enables to make a concrete link between the two-dimensional discrete critical systems from statistical physics and conformal field theory.

Keywords

Cite

@article{arxiv.math/0209382,
  title  = {Conformal fields, restriction properties, degenerate representations and SLE},
  author = {Roland Friedrich and Wendelin Werner},
  journal= {arXiv preprint arXiv:math/0209382},
  year   = {2007}
}

Comments

To appear in C.R.Acad. Sci. Paris, Ser. I Math. Minor modifications from the first version