Establish whether defectsymmetry mismatch occurs in concrete lattice and field-theory realizations

Determine whether the mismatch between defect reduction and symmetry reduction predicted by anomaly matching is realized in specific lattice Hamiltonians and quantum field theories.

Background

For anomaly matching, the paper allows distinct integers R and U governing the preservation of symmetries and defects, while the pairing condition requires R=U. The authors derive this distinction algebraically but do not provide a concrete Hamiltonian or field-theoretic realization demonstrating the mismatch.

References

We do not provide a conclusive discussion of whether such a discrepancy can be realized in lattice models in a specific Hamiltonian of the lattice models or quantum field theories.

— Difference between pair creation and anomaly matching: Nontrivial aspects of invertible symmetries and defects in $SU(N)$ models  (2610.21478 - Fukusumi et al., 15 Oct 2026) in Section 4, “Anomaly matching condition: Mismatch between symmetry and defect”