Random-cluster interfaces: critical, disordered, thermal, and natural-time scaling

Proves chordal SLE_κ limits for critical square-lattice random-cluster interfaces for $0\lt q\le4$, with $\kappa=4\pi/\arccos(-\sqrt q/2)$: bounded Jordan domains are allowed for q ≥ 1, and smooth Jordan domains for q < 1, under the stated marked-boundary approximations. For $1\le q\le4$, complete nested plane loops converge to CLE_κ.