Topological BF field theory description of topological insulators

► We show that a BF theory is the effective theory of 2D and 3D topological insulators. ► The non-gauge-invariance of the bulk theory yields surface terms for a bosonized Dirac fermion. ► The “axion” term in electromagnetism is correctly obtained from gapped surfaces. ► Generalizations to possible fractional phases are discussed in closing.