Fluctuations in finite density holographic quantum liquids

We study correlators of the global U(1) currents in holographic models which involve N=4 SYM coupled to the finite density matter in the probe brane sector. We find the spectral density associated with the longitudinal response to be exhausted by the zero sound pole and argue that this could be consistent with the behavior of Fermi liquid with vanishing Fermi velocity. However the transversal response shows an unusual momentum independent behavior. Inclusion of magnetic field leads to a gap in the dispersion relation for the zero sound mode propagating in the plane of magnetic field. For small values of the magnetic field B the gap in the spectrum scales linearly with B, which is consistent with Kohn's theorem for nonrelativistic fermions with pairwise interaction. We do not find signatures of multiple Landau levels expected in Landau Fermi liquid theory. We also consider the influence of generic higher derivative corrections on the form of the spectral function.