A bulk-boundary correspondence for non-invertible symmetries

Abstract: The notion that symmetry in a d-dimensional QFT is naturally described by placing this QFT at the boundary of a d+1 dimensional TQFT has been very powerful in understanding generalized symmetry actions, particularly for non-invertible symmetries. I discuss a concrete family of models in 2 spatial dimensions, which can be viewed on the one hand as Hamiltonian models describing bulk topological orders, and on the other hand (when the bulk is in its ground state) as bulk TQFT’s describing a symmetry action at the boundary. I will describe how to add additional symmetry by “shading” and “completing” the bulk models. This leads to models which realize interesting symmetries in an onsite manner. Specifically, in the bulk, these shaded models realize symmetries that permute the anyons in the underlying TQFT. At the boundary, these symmetries can take the form of generalized Kramers-Wannier dualities in the boundary spin model. I will illustrate how this works in a few simple examples.

HEP - phenomenologyHEP - theorymathematical physics

Audience: researchers in the topic

NHETC Seminar

Series comments: Description: Weekly research seminar of the NHETC at Rutgers University

Livestream link is available on the webpage.