  Topological phases of matter can be classified by using Clifford algebras
through Bott periodicity. We consider effective topological field theories of
quantum Hall systems and topological insulators that are Chern-Simons and BF
field theories. The edge states of these systems are related to the gauge
invariance of the effective actions. For the edge states at the interface of
two topological insulators, transgression field theory is proposed as a gauge
invariant effective action. Transgression actions of Chern-Simons theories for
(2+1)D and (4+1)D and BF theories for (3+1)D are constructed. By using
transgression actions, the edge states are written in terms of the bulk
connections of effective Chern-Simons and BF theories.
