’t Hooft Anomaly Detection in 2+1d Lattice Systems

I will discuss two methods for diagnosing ’t Hooft anomalies of internal symmetries in 2+1d lattice systems. Anomalous symmetries of this kind arise naturally at the boundary of 3+1D symmetry-protected topological phases, and are known to be classified by the group cohomology of the symmetry group. The first method is purely kinematical: using only the form of the symmetry operators themselves, the anomaly cocycle is computed via a concrete procedure of operator truncation and dimensional reduction. The second method is dynamical in nature, entailing a choice of Hamiltonian that spontaneously breaks the symmetry. The anomaly is exposed in the algebraic structure of the ensuing domain wall excitations.