  We develop a scheme to make exactly solvable gauge theories whose electric
flux lines host (1+1)-dimensional topological phases. We use this exact
`decorated-string-net' framework to construct several classes of interesting
models. In particular, we construct an exactly solvable model of a quantum spin
liquid whose (gapped) elementary excitations form doublets under an internal
symmetry, and hence may be regarded as spin-carrying spinons. The model may be
formulated, and is solvable, in any number of dimensions, on any bipartite
graph. Another example, in any dimension, has $Z_2$ topological order and
anyons which are Kramers' doublets of time reversal symmetry. Further, we make
exactly solvable models of 3d topological paramagnets.
