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Schramm Loewner Evolution and Liouville Quantum Gravity

We conformally weld (via "quantum zipping") two boundary arcs of a Liouville quantum gravity random surface to generate a random curve called the Schramm-Loewner evolution (SLE). We develop a theory of quantum fractal measures (consistent with the Knizhnik-Polyakov-Zamolochikov relation) and analyze their evolution under welding via SLE martingales. As an application, we construct the natural quantum length and boundary intersection measures on the SLE curve itself.

preprint2010arXivOpen access
Bertrand DuplantierScott Sheffield
cond-mat.stat-mechmath.CVmath-phmath.PRmath.MP
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Bertrand DuplantierScott Sheffield

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