  We study the Wegner-Wilson loops in the string-net model of Levin and Wen in
the presence of a string tension. The latter is responsible for a phase
transition from a topological deconfined phase (weak tension) to a trivial
confined phase (strong tension). We analyze the behavior of all Wegner-Wilson
loops in both limiting cases for an arbitrary input theory of the string-net
model. Using a fluxon picture, we compute perturbatively the first
contributions to a perimeter law in the topological phase as a function of the
quantum dimensions. In the trivial phase, we find that Wegner-Wilson loops obey
a modified area law, in agreement with a recent mean-field approach.
