Schramm-Loewner evolution and Liouville quantum gravity.
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.
Institut de Physique Théorique, CEA/Saclay, Gif-sur-Yvette, France.
Bertrand
B
Duplantier
Scott
S
Sheffield