Speaker: Corey Jones (North Carolina State University)
Title: SymTFT on the lattice (in infinite volume)
Abstract: In this talk, we will explain our approach for defining SymTFT decompositions of 1+1D lattice systems directly in the infinite volume limit using algebras of quasi-local operators. The idea is to axiomatize when a subalgebra of the quasi-local algebra can be thought of as observables localized near the physical boundary of some SymTFT decomposition. By focusing directly on the symmetric subalgebra, our formalism is agnostic to the form of the actual symmetry operators (MPO's, weak Hopf algebra, etc.) and includes all examples of UV lattice fusion category symmetries we are aware of. The key technical ingredient is the theory of DHR bimodules of quasi-local algebras, which allow us to formally consider sectors of non-local (but localized) operators (sometimes called ``patch operators" in the literature), which assemble into a UMTC describing the bulk SymTFT. As corollaries, we obtain formal versions of several well-known anomaly enforced gaplessness results from the physics literature, but also some new results, including that a fusion category can be realized as symmetries on a tensor product Hilbert space (without projecting to some sector) if and only if it is integral. Based on joint work with David Evans.