Consistent symmetry breaking and topological phases
arXiv:2607.28181
The paper studies operators that are invariant under a symmetry group and shows that their equivariant indices must remain consistent when the symmetry is reduced to a finite‑index subgroup, establishing a weak/strong dichotomy for these indices and linking the results to topological insulators and coarse‑geometric index theory.
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.