Anton Kapustin

Speaker at the Spring Time in Mathematical Quantum Physics Workshop ( UBC, May 2025)

Title: Topological invariants of quantum lattice systems and ’t Hooft anomalies

Abstract: The conjectured relationship between gapped lattice systems and TQFT implies that such systems may have topological invariants: numerical quantities which do not vary under deformations which do not close the gap. An example of such an invariant is zero-temperature Hall conductance of a 2d system with U(1) symmetry. In this talk I will explain that such invariants can be interpreted as obstructions to promoting a symmetry of a gapped state to an approximately local symmetry, i.e. as lattice avatars of ’t Hooft anomalies. To make this precise, I axiomatize the notions of a local symmetry and of an approximately local symmetry. As an application, I will define topological invariants of gapped lattice systems living on arbitrary asymptotically conical regions of Euclidean space.