  We consider the $D4-D8-\bar{D8}$ brane system which serves as ultraviolet
completion of the Nambu-Jona-Lasinio model, where the only degrees of freedom
carrying baryon charge are fermions. By turning on chemical potential for this
charge one may expect the formation of the Fermi liquid ground state. At strong
coupling we use the dual holographic description to investigate the responses
of the system to small perturbations. In the chirally symmetric phase we find
that the density dependent part of the heat capacity vanishes linearly with
temperature. We also observe a zero sound excitation in the collisionless
regime, whose speed is equal to that of normal sound in the hydrodynamic
regime. Both the linear dependence of the heat capacity and the existence of
zero sound are properties of the Fermi liquid ground state. We also compute the
two-point function of the currents at vanishing frequency but do not find any
singularities at finite values of the momentum.
