Topological orders with classical Lie group symmetries from coupling electron wires

We study the topological order that arises from chiral states with SU(N) or SO(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 $\mathrm{SU}{(m)}_{n}, \mathrm{SO}{(m)}_{n}$, or $\mathrm{Sp}{(m)}_{n}$ 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.