Conformal fields, restriction properties, degenerate representations and SLE. (English. Abridged French version) Zbl 1101.81095
Summary: We relate the Schramm–Loewner Evolution processes (SLE) to highest-weight representations of the Virasoro algebra. The restriction properties of SLE that have been recently derived in [G.F. Lawler, O. Schramm, Wendelin Werner, J. Am. Math. Soc. 16, No. 4, 917–955 (2003; Zbl 1030.60096)] play a crucial role. In this setup, various considerations from conformal field theory can be interpreted and reformulated via SLE. This enables one to make a concrete link between the two-dimensional discrete critical systems from statistical physics and conformal field theory.
MSC:
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 60G07 | General theory of stochastic processes |
| 81R10 | Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations |
| 81T27 | Continuum limits in quantum field theory |
Citations:
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