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2014

Gapped Domain Walls, Gapped Boundaries and Topological Degeneracy

Lan, Tian, Wang, Juven, Wen, Xiao-Gang

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Gapped domain walls, as topological line defects between 2+1D topologically ordered states, are examined.

We provide simple criteria to determine the existence of gapped domain walls, which apply to both Abelian and non-Abelian topological orders.
Our criteria also determine which 2+1D topological orders must have gapless edge modes, namely which 1+1D global gravitational anomalies ensure gaplessness.
Furthermore, we introduce a new mathematical object, the tunneling matrix $\mathcal W$, whose entries are the fusion-space dimensions $\mathcal W_{ia}$, to label different types of gapped domain walls.

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