Topological orders with classical Lie group edge symmetries from coupling electron wires

We extend our previous work, studying the topological order that descends from the bosonic E_8 quantum Hall state, to states with SU(N), SO(N), and Sp(N) edge-state symmetries. This allows us to provide a systematic, microscopic understanding for the emergence of quantum Hall states, topological superconductors, and spin liquids with non-Abelian quasiparticle excitations of the Majorana, metaplectic, and Fibonacci type. We do this using exactly solvable models of coupled electron wires. This allows explicit interactions that result in SU(m)_n, SO(m)_n and Sp(m)_n topological orders with arbitrary levels.