Topological orders with classical Lie group symmetries from coupling electron wires

We study the topological order that arises from chiral states with $\mathrm{S}\mathrm{U}(N)$ or $\mathrm{S}\mathrm{O}(N)$ edge-state symmetry. This extends our previous study of topological orders that descend from the bosonic $E_8$ quantum Hall state. We use exactly solvable models of coupled electron wires to construct states with $\mathrm{S}\mathrm{U}(m{)}_n$, $\mathrm{S}\mathrm{O}(m{)}_n$, or $\mathrm{S}\mathrm{p}(m{)}_n$ topological order for various levels $n$. We use our constructions to write down string operators for various non-Abelian anyons. We thereby provide a systematic, model derivation of quantum Hall states, topological superconductors, and spin liquids with emergent non-Abelian quasiparticle excitations, including those of Ising, metaplectic, and Fibonacci type.