Radial conformal welding in Liouville quantum gravity

TL;DR

This paper extends the theory of conformal welding in Liouville quantum gravity to the radial case, linking it with imaginary geometry and radial SLE curves.

Contribution

It introduces a new framework for radial conformal welding in LQG, expanding the understanding of interface structures in quantum surfaces.

Findings

Established radial conformal welding in LQG.

Connected radial welding with imaginary geometry and SLE.

Enhanced the mathematical understanding of quantum surface interfaces.

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.