Journal of Statistical Physics

, Volume 123, Issue 6, pp 1169–1181 | Cite as

On Conformal Field Theory of SLE(κ,ρ)

  • Kalle Kytölä


SLE(κ ρ), 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(κ ρ) describes an interface in a statistical mechanics model whose boundary conditions are created in the Coulomb gas formalism by vertex operators with charges α j = \(\alpha_j = \frac{\rho_j}{2 \sqrt{\kappa}}\). The total charge vanishes and therefore the partition function has a simple product form. We also suggest a generalization of SLE(κ ρ)


SLE conformal field theory 


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Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of HelsinkiHelsinkiFinland

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