Radial conformal welding in Liouville quantum gravity

Abstract

The seminal work of Sheffield showed that when random surfaces called Liouville quantum gravity (LQG) are conformally welded, the resulting interface is Schramm-Loewner evolution (SLE). This has been proved for a variety of configurations, and has applications to the scaling limits of random planar maps and the solvability of SLE and Liouville conformal field theory. We extend the theory to the setting where two sides of a canonical three-pointed LQG surface are conformally welded together, resulting in a radial SLE curve which can be described by imaginary geometry.