Effective field theories for topological insulators by functional bosonization

Effective field theories that describe the dynamics of electric current for topological insulators in general dimension D = d+1 are discussed using the functional bosonization. For non-interacting topological insulators with a conserved U(1) charge and characterized by an integer topological invariant, we derive the BF-type topological field theories supplemented with the Chern-Simons (when D is odd) or the Axion term (when D is even). For topological insulators characterized by a Z2 topological invariant, their topological field theories are obtained by dimensional reduction. Building on this effective field theory description for non- interacting topological phases, we also discuss, following the spirit of the parton construction of the fractional quantum Hall effect, the putative ``fractional'' topological insulators and their possible effective field theories.