Dubédat's SLE boundary duality conjecture

Let κ4\kappa\geq 4, and let SLEσ(κ,κ4)SLE^\sigma(\kappa,\kappa-4) be the reflection-symmetric image of SLE(κ,κ4)SLE(\kappa,\kappa-4) in the upper half-plane. Let R\partial_R denote its right boundary, and set

κ=16κ.\kappa'=\frac{16}{\kappa}.

Dubédat's boundary duality conjecture. The right boundary of SLEσ(κ,κ4)SLE^\sigma(\kappa,\kappa-4) is an SLE(κ,(κ4)/2)SLE(\kappa',(\kappa'-4)/2). The conjecture is a precise proposed realization of SLE duality through an SLE with force point; the source presents it as proposed by Dubédat and does not claim a proof.

Sources & referencesView supporting material

Primary source

Wendelin Werner, “Conformal restriction and related questions”, arXiv:math/0307353 (2003).

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