  We report on a potentially new class of non-Fermi liquids in
(2+1)-dimensions. They are identified via the response functions of composite
fermionic operators in a class of strongly interacting quantum field theories
at finite density, computed using the AdS/CFT correspondence. We find strong
evidence of Fermi surfaces: gapless fermionic excitations at discrete shells in
momentum space. The spectral weight exhibits novel phenomena, including
particle-hole asymmetry, discrete scale invariance, and scaling behavior
consistent with that of a critical Fermi surface postulated by Senthil.
