Tue, Jan 12, 2016, 1:00 pm to 2:00 pm
Abstract: Quantum matter in two spatial dimensions can exhibit topological order, which supports quasiparticles excitations with anyonic statistics and fractional symmetry quantum numbers, the latter of which is a manifestation of symmetry-enriched topological order. In this talk I will examine the interplay between global symmetry and topologically ordered phases. I will describe a general theory of how symmetry acts on emergent topological degrees of freedom, classifying different ways that quasiparticles may carry fractionalized quantum numbers. For on-site unitary symmetry, a systematic theory of extrinsic symmetry defects is developed to determine their topological properties, such as the braiding exchange transformations. The general framework also identifies two obstructions or “anomalies”, one for the inability to fractionalize a topological symmetry, and the other one for the existence of symmetry defects. I will then describe some applications of the theory to understanding parafermion zero modes in fractional quantum Hall states, and to the problem of classifying fermionic symmetry-protected phases in two dimensions.