SLEs as boundaries of clusters of Brownian loops

In this research announcement, we show that SLE curves can in fact be viewed as boundaries of certain clusters of Brownian loops (of the clusters in a Brownian loop soup). For small densities c of loops, we show that the outer boundaries of the clusters created by the Brownian loop soup are SLE κ -type curves where κ ∈(8/3,4] and c related by the usual relation c =(3 κ −8)(6− κ )/2 κ (i.e., c corresponds to the central charge of the model). This gives (for any Riemann surface) a simple construction of a natural countable family of random disjoint SLE κ loops, that behaves “nicely” under perturbation of the surface and is related to various aspects of conformal field theory and representation theory.