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We construct Cardy states, defect lines and chiral operators for rationalcoset conformal field theories on the lattice. The bulk theory is obtained bytaking the overlap between tensor network representations of differentstring-nets, while the primary fields emerge from using the topologicalsuperselection sectors of the anyons in the original topological theory. Thismapping provides an explicit manifestation of the equivalence between conformalfield theories in two dimensions and topological field theories in threedimensions: their groundstates and elementary excitations are represented byexactly the same tensors.

Cardy states, defect lines and chiral operators of coset CFTs on the lattice