Topological BF field theory description of topological insulators

Understand

Topological phases of matter are described universally by topological field theories in the same way that symmetry-breaking phases of matter are described by Landau-Ginzburg field theories.

• We propose that topological insulators in two and three dimensions are described by a version of abelian $BF$ theory.
• For the two-dimensional topological insulator or quantum spin Hall state, this description is essentially equivalent to a pair of Chern-Simons theories, consistent with the realization of this phase as paired integer quantum Hall effect states.
• The $BF$ description can be motivated from the local excitations produced when a $\pi$ flux is threaded through this state.