  We construct Cardy states, defect lines and chiral operators for rational
coset conformal field theories on the lattice. The bulk theory is obtained by
taking the overlap between tensor network representations of different
string-nets, while the primary fields emerge from using the topological
superselection sectors of the anyons in the original topological theory. This
mapping provides an explicit manifestation of the equivalence between conformal
field theories in two dimensions and topological field theories in three
dimensions: their groundstates and elementary excitations are represented by
exactly the same tensors.
