A Non-Fermi Liquid from a Charged Black Hole; A Critical Fermi Ball

Using the AdS/CFT correspondence, we calculate a fermionic spectral function in a 2+1 dimensional non-relativistic quantum field theory which is dual to a gravitational theory in the $AdS_4$ background with a charged black hole. The spectral function shows no quasiparticle peak but the Fermi surface is still well defined. Interestingly, all momentum points inside the Fermi surface are critical and the gapless modes are defined in a {\it critical Fermi ball} in the momentum space.