Microscopic Constructions of the BF+AAB Topological Field Theory and Borromean-Rings Braiding in (3+1) Dimensions
The research establishes an exact link between a continuum topological field theory (BF theory with an AAB twist) and a microscopic lattice model (the D4 quantum double). This correspondence proves that complex topological operations, such as fusion rules, shrinking rules, and exotic Borromean-Rings braiding statistics, are perfectly realized on the lattice. This bridges the gap between continuous field theories and discrete microscopic systems.