Effective field theories for topological insulators via functional bosonization
Seminar Room 1, Newton Institute
Eﬀective ﬁeld theories that describes the dynamics of a conserved U(1) current in terms of “hydrodynamic” degrees of freedom of topological phases in condensed matter are discussed in general dimension D = d+1 using the functional bosonization technique. For non-interacting topological insulators (superconductors) 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 θ-term (when D is even). For topological insulators characterized by a Z2 topological invariant (the ﬁrst and second descendants of the primary series), their topological ﬁeld theories are obtained by dimensional reduction. Building on this eﬀective ﬁeld theory description for noninteracting topological phases, we also discuss, following the spirit of the parton construction of the fractional quantum Hall eﬀect by Block and Wen, the putative “fractional” topological insulators and their possible eﬀective ﬁeld theories, and use them to determine the physical properties of these.