Fractional topological insulators: From sliding Luttinger liquids to Chern-Simons theory

The sliding Luttinger liquid approach is applied to study fractional topological insulators (FTIs). We show that a FTI is the low energy fixed point of the theory for realistic spin-orbit and electron-electron interactions. We find that the topological phase pertains in the presence of an interaction that breaks the spin invariance, and its boundaries are even extended by those terms. Finally we show that the one-dimensional chiral anomaly in the Luttinger liquid leads to the emergence of topological Chern-Simons terms in the effective gauge theory of the FTI state.