Classifying three dimensional symmetry enriched topological phases via topological field theory*

While two dimensional symmetry enriched topological phases(SET) have been intensively studied, many issues of the three dimensional ones are still open. In this talk, we are going to focus on the 3 dimensinoal abelian topological order enriched by abelian symmetries and try to classify those phases via topological field theory. Three dimensional ablian topological orders can be described by topological BF field theory. Different abelian topological orders correspond inequivalent BF field theories. We found that imposing the symmetry in the topological theory, the number of inequivalent theories without breaking symmetry may increase, saying the topological orders are enriched. To classify all these inequivalent 3D SET phases, we gauge the symmetry and study the resulting phases.