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Conformal Restriction, Highest-Weight Representations and SLE

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We show how to relate Schramm-Loewner Evolutions (SLE) to highest-weight representations of infinite-dimensional Lie algebras that are singular at level two, using the conformal restriction properties studied by Lawler, Schramm and Werner in [33]. This confirms the prediction from conformal field theory that two-dimensional critical systems are related to degenerate representations.

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Authors and Affiliations

  1. Laboratoire de Mathématiques, Université Paris-Sud, 91405, Orsay cedex, France

    Roland Friedrich & Wendelin Werner

  2. I.H.E.S., 35, route de Chartres, 91440, Bures-sur-Yvette, France

    Roland Friedrich

  3. Institut Universitaire de France

    Wendelin Werner

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  1. Roland Friedrich
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  2. Wendelin Werner
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Correspondence to Wendelin Werner.

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Communicated by A. Kupiainen

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Friedrich, R., Werner, W. Conformal Restriction, Highest-Weight Representations and SLE. Commun. Math. Phys. 243, 105–122 (2003). https://doi.org/10.1007/s00220-003-0956-8

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