From gauge to higher gauge models of topological phases

Understand

We consider exactly solvable models in (3+1)d whose ground states are described by topological lattice gauge theories.

• Using simplicial arguments, we emphasize how the consistency condition of the unitary map performing a local change of triangulation is equivalent to the coherence relation of the pentagonator 2-morphism of a monoidal 2-category.
• By weakening some axioms of such 2-category, we obtain a cohomological model whose underlying 1-category is a 2-group.
• Topological models from 2-groups together with their lattice realization are then studied from a higher gauge theory point of view.