Gapped domain walls, gapped boundaries, and topological degeneracy.

摘要: Gapped domain walls, as topological line defects between (2+1)D topologically ordered states, are examined. We provide simple criteria to determine the existence of gapped which apply both Abelian and non-Abelian orders. Our also orders must have gapless edge modes, namely, (1+1)D global gravitational anomalies ensure gaplessness. Furthermore, we introduce a new mathematical object, tunneling matrix W, whose entries fusion-space dimensions W(ia), label different types walls. By studying many examples, find evidence that matrices powerful quantities classify Since boundary is wall bulk order vacuum, regarded trivial order, our theory walls inclusively contains boundaries. In addition, derive ground state degeneracy formula, applied arbitrary orientable spatial 2-manifolds with including closed open