(3+1)-TQFTs and Topological Insulators

Understand

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.