Random surface, planar lattice model, and conformal field theory
Random surface, planar lattice model, and conformal field theory
In-Person Talk
Liouville quantum gravity (LQG) is aÌýtheoryÌýofÌýrandomÌýsurfaces that originated from stringÌýtheory. Schramm Loewner evolution (SLE) is a family ofÌýrandomÌýplanarÌýcurves describing scaling limits of many 2DÌýlatticeÌýmodelsÌýat their criticality. Before the rigorous study via LQG and SLE inÌýprobability,ÌýrandomÌýsurfaces and scaling limits ofÌýlatticeÌýmodels have been studied via Ìýanother approach in theoretical physics calledÌýconformalÌýfieldÌýtheoryÌý(CFT) since the 1980s. In this talk, I will demonstrate how a combination of ideas from LQG/SLE and CFT can be used to rigorously prove several long standingÌýpredictions in physics onÌýrandomÌýsurfaces andÌýplanarÌýlatticeÌýmodels, includingÌýthe law of theÌýrandomÌýmodulus of the scaling limit of uniform triangulationÌýof the annular topology, and the crossing formula for criticalÌýplanarÌýpercolation on an annulus. I will then present some conjectures which further illustrate the deep and rich interaction between LQG/SLE and CFT.Ìý
Based on joint works with Ang, Holden, Remy, Xu, and Zhuang.
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