IAS CMP/QFT Group Meeting

Abstract: Higher-form symmetry in a tensor product Hilbert space is always emergent: the symmetry generators become topological only when the Gauss law is energetically enforced at low energies. In this talk, I explain a general method for defining the 't Hooft anomaly of higher-form symmetries in lattice models built on a tensor product Hilbert space. For instance, this allows us to define an index valued in $H^4(B^2G, U(1))$ characterizing the ’t Hooft anomaly of 1-form symmetry (2+1)D, for given finite depth circuits generating the symmetry. I also outline a criteria for “onsiteability” of higher-form symmetry.