(3+1)-TQFTs and topological insulators

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.

Keywords

topological quantum field theory (TQFT) / topological insulator / premodular category

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2014 Higher Education Press and Springer-Verlag Berlin Heidelberg