Consistent symmetry breaking and topological phases
Yuezhao Li, Guo Chuan Thiang
Abstract
Operators invariant under a symmetry group are also invariant under any finite-index subgroup. The equivariant indices of such operators must be consistent under symmetry breaking. We use this principle to establish a canonical weak/strong dichotomy for equivariant indices, building on an idea originating in the theory of topological insulators in solid-state physics. We also study the relationship to coarse-geometric, or macroscopic, indices.
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