Exotic quantum wires from symmetry-enriched topological order interfaces*

When two identical chiral topological orders merge, the gapless modes at their interface can annihilate—thereby forming a single, uninterrupted topological phase. We study such interfaces when one of the two phases is promoted to a symmetry-enriched topological order exhibiting an anyon-permuting symmetry. In this case symmetry provides an obstruction to gapping the interface; moreover, we show that the gapless, symmetry-preserving interface can realize nontrivial critical points with no fine-tuning required. Such exotic "quantum wires" can provide efficient building blocks for assembling two-dimensional topological orders hosting anyons with universal braid statistics.