Topological Invariants of Gapped States and 't Hooft Anomalies

Explore a one-hour lecture on topological invariants of gapped ground-states in lattice systems, presented by Anton Kapustin at the Institut des Hautes Etudes Scientifiques (IHES). Delve into the recently developed approach for constructing these invariants, which applies to arbitrary gapped states of infinite-volume lattice spin systems with rapidly decaying interactions. Discover how C*-algebraic techniques are employed in this method. Gain insights into the interpretation of these invariants as obstructions to gauging, or promoting a symmetry to a local symmetry. Examine the key observation that locality on a lattice is an asymptotic notion sensitive only to the large-scale geometry of the support set. Learn about the use of Kashiwara and Schapira's natural Grothendieck topology on a category of semilinear subsets of Euclidean space to encode locality. Understand how infinitesimal symmetries of a gapped state form a cosheaf over the corresponding site, and how topological invariants are encoded in its Cech complex. Access this and other scientific videos on the French platform CARMIN.tv, which offers additional functionalities tailored for the research community.

Anton Kapustin - Topological Invariants of Gapped States and ’t Hooft Anomalies