Classification of SPT/SET orders: boundary-bulk relation and higher categories

Abstract

It is known that 2d (spatial dimension) symmetry protected topological (SPT) orders and symmetry enriched topological (SET) orders with finite onsite symmetries can be characterized by using the idea of gauging the symmetry and minimal modular extensions. In this talk, I will introduce another characterization of SPT/SET orders in all dimensions based on the boundary-bulk relation. In 1d, this result recovers the well-known classification of 1d SPT/SET orders. For 2d SPT/SET orders, this result gives a 2-categorical point of view of minimal modular extensions. In higher dimensions, we also obtain many precise mathematical conjectures on higher categories. If time permits, I will briefly introduce a new characterization of SPT/SET orders in the language of enriched categories.