Gauging the Kramers–Wannier non-invertible symmetry in the critical Ising lattice model

Ascertain whether a well-defined gauging procedure exists for the Kramers–Wannier non-invertible symmetry in the 1+1-dimensional critical transverse-field Ising lattice model, whose symmetry mixes with lattice translations; either explicitly construct such a gauging procedure or rigorously prove that gauging is impossible due to the associated ’t Hooft anomaly implied by Lieb–Schultz–Mattis–type constraints.

Background

The paper studies gauging finite non-invertible symmetries on 1+1d lattice Hamiltonians and uses Rep(D8) as the simplest anomaly-free example realizable on a spin chain of qubits. In contrast, the canonical Kramers–Wannier (KW) non-invertible symmetry appearing in the critical transverse-field Ising model mixes with lattice translations, which complicates defining a standard gauging procedure.

The authors note that this mixing raises doubts about whether a well-defined gauging exists for the KW symmetry. They further observe that Lieb–Schultz–Mattis–type constraints signal an ’t Hooft anomaly, suggesting an obstruction to gauging. Determining definitively whether a consistent gauging can be formulated—or proving a no-go theorem—remains an explicit unresolved issue highlighted in the text.