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We demonstrate how to obtain integrable results for the Schramm-Loewner evolution (SLE) from Liouville conformal field theory (LCFT) and the mating-of-trees framework for Liouville quantum gravity (LQG).
Convergence of uniform triangulations under the Cardy embedding
N. Holden and X. Sun · 1905
Earlier work this paper cites.
Mating of trees for random planar maps and Liouville quantum gravity: a survey
E. Gwynne, N. Holden, and X. Sun · 1910
Earlier work this paper cites.
Unit boundary length quantum disk: a study of two different perspectives and their equivalence
B. Cerclé · 1912
Earlier work this paper cites.
Quantum geometry of bosonic strings
A. M. Polyakov · 1981
Earlier work this paper cites.
Infinite conformal symmetry in two-dimensional quantum field theory
A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov · 1984
Earlier work this paper cites.
Poisson processes
J. F. C. Kingman · 1993
Earlier work this paper cites.
Two- and three-point functions in Liouville theory
H. Dorn and H.-J. Otto · 1994
Earlier work this paper cites.
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J. Teschner · 1995
Earlier work this paper cites.
Conformal bootstrap in Liouville field theory
A. Zamolodchikov and A. Zamolodchikov · 1996
Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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J. Dubédat · 2005
Earlier work this paper cites.
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C. Guillarmou, A. Kupiainen, R. Rhodes, and V. Vargas · 2005
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Conformally invariant processes in the plane
G. F. Lawler · 2005
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Excursion decompositions for SLE and Watts’ crossing formula
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N. Berestycki · 2017
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V. Vargas · 2017
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