Schramm-Loewner Evolution and Liouville Quantum Gravity
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Duplantier-2011-Letters-Schramm-Loewner Evolution and Liouville Quantum Gravity.pdf
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Author(s) •
Duplantier, Bertrand
Sheffield, Scott Roger
Date Issued
September 2011
Journal
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
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1103/PhysRevLett.107.131305