Fractional Quantum Hall edge modes from topological fluid dynamics

The dynamics of Fractional Quantum Hall (FQH) states with filling factor $ u=frac{1}{2k+1}$ can be expressed in terms of hydrodynamic equations with an additional constitutive relation, which constrains the flow vorticity to fluctuations of the condensate density (Hall constraint). Therefore, starting from this dissipationless hydrodynamic system, we study which boundary conditions are compatible with the gauge anomaly at the edge of the FQH sample. We show that, in the hard wall interface, the anomaly inflow mechanism is fundamentally incompatible with the no-slip condition, that is, when the fluid sticks to the wall. Moreover, we obtain that the gauge anomaly introduces tangential forces on the boundary which can be canceled by fluid stresses. In the absence of tangent external electric fields, these stresses vanish, which allows the fluid to slip at the wall with no friction. In this limit, that no-stress condition gives rise to a dispersive chiral hydrodynamic edge mode, which is of the form $omega=c_1 k+c_2 k^3$, and a spurious non-dispersive mode which is incompatible with the anomaly inflow mechanism. At the end, we discuss the non-linear dynamics of this edge mode.