13:00
Non-invertible symmetry: from rational CFTs to the lattice
Abstract
Finite non-invertible symmetries have been extensively studied in both (1+1)-dimensional conformal field theories and quantum lattice systems. The kinematics of these settings look very different. We will show that nevertheless, for a class of rational CFT symmetries preserving a common rational chiral algebra, the continuum and lattice descriptions are exactly equivalent in a precise sense. The main idea is to encode symmetry through the inclusion of symmetry-invariant observables into the full observable algebra. After adjoining symmetry-trivial infinite-dimensional degrees of freedom to an anyon chain, these inclusions can be identified by an isomorphism of algebras that preserves locality up to a uniformly bounded enlargement of regions in both directions. Starting from familiar examples of CFT defects and anyon chains, we will explain this equivalence, the resulting classification of local symmetry structures by fusion categories, and its implications for transporting states and dynamics between the continuum and the lattice.