Joint CLE scaling limit of FK interfaces on random planar maps

Establish that the loops separating primal and dual clusters in suitably renormalised self-dual FK(q)-weighted planar maps converge jointly with the map to an independent conformal loop ensemble with parameter kappa' = 16/gamma^2.

Background

In addition to the conjectured convergence of the underlying maps to a Liouville quantum gravity surface, the paper identifies a conjectural scaling limit for the interfaces separating primal and dual FK clusters. The proposed limit is an independent CLE with parameter determined by the LQG parameter.

The paper cites peanosphere-topology convergence and several exponent calculations as supporting evidence, but does not prove the asserted joint convergence of the map and loop ensemble. This remains an explicitly stated conjectural problem.