The SLE loop via conformal welding of quantum disks

We prove that the SLE? loop measure arises naturally from conformal welding of two ?-Liouville quantum gravity (LQG) disks for ?2=??(0,4). The proof relies on our companion work LQG and uses as an essential tool concept uniform embedding surfaces. Combining result with Gwynne Miller, we get random quadrangulations decorated by a self-avoiding polygon converge in scaling limit to sphere SLE8?3 loop. Our is also key input recent first third coauthors integrability ensemble.