Consistent symmetry breaking and topological phases
Mathematical Physics
2026-07-30 v1 Mesoscale and Nanoscale Physics
K-Theory and Homology
Metric Geometry
Operator Algebras
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.
Cite
@article{arxiv.2607.28181,
title = {Consistent symmetry breaking and topological phases},
author = {Yuezhao Li and Guo Chuan Thiang},
journal= {arXiv preprint arXiv:2607.28181},
year = {2026}
}