On conformal field theory of SLE(kappa; rho)

Abstract

SLE(kappa; rho), a generalization of chordal Schramm-Löwner evolution (SLE), is discussed from the point of view of statistical mechanics and conformal field theory (CFT). Certain ratios of CFT correlation functions are shown to be martingales. The interpretation is that SLE(kappa; rho) describes an interface in a statistical mechanics model whose boundary conditions are created in the Coulomb gas formalism by vertex operators with charges alpha = rho/(2 sqrt(kappa)). The total charge vanishes and therefore the partition function has a simple product form. We also suggest a generalization of SLE(kappa; rho).

arXiv comment13 pages. Several minor changes and some reorganization: corrections of misprints, added references and changes suggested by reviewers

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• The scaling limit of two cluster boundaries in critical lattice models
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• SLE local martingales, reversibility and duality
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• CFT Interpretation of Merging Multiple SLE Traces
• Conformal field theory on the Riemann sphere and its boundary version for SLE
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