(3+1)-TQFTs and Topological Insulators
arXiv:1104.2632
Abstract
Levin-Wen models are microscopic spin models for topological phases of matter in (2+1)-dimension. We introduce a generalization of such models to (3+1)-dimension based on unitary braided fusion categories, also known as unitary premodular categories. We discuss the ground state degeneracy on 3-manifolds and statistics of excitations which include both points and defect loops. Potential connections with recently proposed fractional topological insulators and projective ribbon permutation statistics are described.
Several clarifications are added. To appear in the special issue of Frontiers of Physics on topological insulators
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- Kitaev models based on unitary quantum groupoids
- Anomaly and Cobordism Constraints Beyond the Standard Model: Topological Force
- Lattice construction of exotic invertible topological phases
- Chiral Edge States Emerging on Anyon-Net