Towards a conformal field theory for Schramm-Loewner evolutions

Abstract

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.

arXiv comment(v2): references updated; final version

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Cited by in corpus (9)

• Crossing Probabilities of Multiple Ising Interfaces
• Large deviations of Schramm-Loewner evolutions: A survey
• UST branches, martingales, and multiple SLE(2)
• Large deviations of multichordal SLE${}_{0+}$, real rational functions, and zeta-regularized determinants of Laplacians
• Connection Probabilities of Multiple FK-Ising Interfaces
• Statistical Mechanics of Confined Polymer Networks
• Uniform Spanning Tree in Topological Polygons, Partition Functions for SLE(8), and Correlations in $c=-2$ Logarithmic CFT
• Irreducible Virasoro representations in Liouville conformal field theory
• Planar UST Branches and $c=-2$ Degenerate Boundary Correlations