Schramm-Loewner Evolution and Liouville Quantum Gravity
Name
Duplantier-2011-Letters-Schramm-Loewner Evolution and Liouville Quantum Gravity.pdf
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167.21 KB
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Checksum (MD5)
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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
Terms of Use
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
