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