Bipolar orientations on planar maps and SLE12.

We give bijections between bipolar-oriented (acyclic with unique source and sink) planar maps and certain random walks, which show that the uniformly random bipolar-oriented planar map, decorated by the .peano curve. surrounding the tree of left-most paths to the sink, converges in law with respect to the peanosphere topology to a 4/3....-Liouville quantum gravity surface decorated by an independent Schramm.Loewner evolution with parameter .=12 (i.e., SLE12). This result is universal in the sense that it holds for bipolar-oriented triangulations, quadrangulations, k-angulations and maps in which face sizes are mixed.