We introduce a class of random compact metric spaces $mathscr{L}_{lpha}$ indexed by $lpha~in(1,2)$ and which we call stable looptrees. They are made of a collection of random loops glued together along a tree structure, and can be informally be viewed as dual graphs of $lpha$-stable Lévy trees. We study their properties and prove in particular that the Hausdorff dimension of $ mathscr{L}_{lpha}$ is almost surely equal to $lpha$. We also show that stable looptrees are universal scaling limits, for the Gromov-Hausdorff topology, of various combinatorial models. In a companion paper, we prove that the stable looptree of parameter $ rac",$ is the scaling limit of cluster boundaries in critical site-percolation on large random triangulations.
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