  We construct and study the conformal loop ensembles CLE(kappa), defined for
all kappa between 8/3 and 8, using branching variants of SLE(kappa) called
exploration trees. The conformal loop ensembles are random collections of
countably many loops in a planar domain that are characterized by certain
conformal invariance and Markov properties. We conjecture that they are the
scaling limits of various random loop models from statistical physics,
including the O(n) loop models.
