Schramm Loewner Evolution and Liouville Quantum Gravity
Dec, 2010Citations per year
Abstract: (arXiv)
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.- 64.60.al
- 02.90.+p
- 02.50.-r
- 04.60.Kz
- quantum gravity
- Liouville
- random surface
- fractal
- measure: quantum
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