Algebraic properties of CFT coset construction and Schramm-Loewner evolution

Abstract

Schramm-Loewner evolution appears as the scaling limit of interfaces in lattice models at critical point. Critical behavior of these models can be described by minimal models of conformal field theory. Certain CFT correlation functions are martingales with respect to SLE. We generalize Schramm-Loewner evolution with additional Brownian motion on Lie group $G$ to the case of factor space $G/A$. We then study connection between SLE description of critical behavior with coset models of conformal field theory. In order to be consistent such construction should give minimal models for certain choice of groups.

10 pages, 2 figures, talk given at the conference "Quantum Theory and Symmetries (QTS-7)"

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• SLE for theoretical physicists
• 2D growth processes: SLE and Loewner chains
• Stochastic Loewner evolution for conformal field theories with Lie-group symmetries
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Cited by in corpus (1)

• Multiple Schramm-Loewner evolutions for conformal field theories with Lie algebra symmetries