Coupled wire models of surface topological orders for ADE classifications, symmetries and dualities

We systematically study 2+1d surface topological orders and their duality and symmetry properties for ADE classes of Lie group theories via coupled wire constructions. We first construct gapped surface topologically ordered systems for ADE classes, by introducing current-current interactions (Gross-Neveu type) on the chiral Luttinger liquid model. We study the property of the ground state and the excitations. Then we perform non-local duality transformations explicitly in terms of the local degrees of freedom on each wire and study properties of the original and dual theories. Most of them are self-dual in the sense that the interactions of both theories have the same form. We also study the symmetry transformation under duality.