Toward a conformal field theory for Schramm-Loewner evolutions. (English) Zbl 1431.82020
Summary: We discuss the partition function point of view for chordal Schramm-Loewner evolutions and their relationship with correlation functions in conformal field theory. Both are closely related to crossing probabilities and interfaces in critical models in two-dimensional statistical mechanics. We gather and supplement previous results with different perspectives, point out remaining difficulties, and suggest directions for future studies.
©2019 American Institute of Physics
©2019 American Institute of Physics
MSC:
| 82C31 | Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics |
| 60J67 | Stochastic (Schramm-)Loewner evolution (SLE) |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 82B26 | Phase transitions (general) in equilibrium statistical mechanics |
| 82B27 | Critical phenomena in equilibrium statistical mechanics |
| 60J65 | Brownian motion |
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
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