Schramm-Loewner Evolution and Liouville Quantum Gravity
Author(s)
Duplantier, Bertrand; Sheffield, Scott Roger
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We show that when two boundary arcs of a Liouville quantum gravity random surface are conformally welded to each other (in a boundary length-preserving way) the resulting interface is a random curve called the Schramm-Loewner evolution. We also develop a theory of quantum fractal measures (consistent with the Knizhnik-Polyakov-Zamolochikov relation) and analyze their evolution under conformal welding maps related to Schramm-Loewner evolution. As an application, we construct quantum length and boundary intersection measures on the Schramm-Loewner evolution curve itself.
Date issued
2011-09Department
Massachusetts Institute of Technology. Department of MathematicsJournal
Physical Review Letters
Publisher
American Physical Society (APS)
Citation
Duplantier, Bertrand, and Scott Sheffield. “Schramm-Loewner Evolution and Liouville Quantum Gravity.” Physical Review Letters 107.13 (2011): n. pag. Web. 27 Jan. 2012. © 2011 American Physical Society
Version: Final published version
ISSN
0031-9007
1079-7114