Relate nonlocal emergent symmetries to microscopic topological data

Determine how nonlocal emergent symmetry groups around the Bott clock are related directly to the exact protecting symmetry group and other topological data of the corresponding fermionic symmetry-protected topological phases.

Background

The discussion notes that emergent symmetries may be approximate manifestations of larger non-on-site, non-compact, or otherwise nonlocal structures. Although such structures have been identified in specific class-DIII examples, their systematic relation to the protecting symmetry and topological invariants throughout the Bott clock remains unresolved.

References

Around the Bott clock, how the non-local emergent symmetry groups are directly related to the exact protecting symmetry $G_p$ and other topological data remains an open question.

— Holographic Representations of Topological Quantum Criticality: Emergent Symmetry Approach around the Bott Clock  (2608.30335 - Yang et al., 31 Aug 2026) in Section 5, Discussions (Section \ref{sec:discussion})