Symmetry fractionalization, defects, and gauging of topological phases

This paper develops a comprehensive theory of symmetry fractionalization together with the properties of symmetry defects in topologically ordered phases of matter in two spatial dimensions. To do this, the authors also introduce the full set of data, consistency conditions, and equivalences for a mathematical theory, known as a G-crossed braided tensor category, that characterizes the algebraic braiding and fusion properties of symmetry defects. This theoretical framework can completely characterize and classify symmetry-enriched topological phases of matter in the presence of arbitrarily strong interactions in quantum many-body systems in two spatial dimensions.