  We find exact, analytic solutions of the Dirac equation for a charged,
massless fermion in the background of a charged, dilatonic black hole in AdS_5.
The black hole descends from type IIB supergravity, where it describes
D3-branes with equal angular momenta in two of the three independent planes of
rotation orthogonal to the world-volume. The Green's function near the Fermi
surface for a strongly coupled fermionic system can be extracted
holographically from an exact solution of the Dirac equation at zero frequency
but nonzero momentum. There can be several Fermi momenta, and they take the
form k_F=q-n-1/2 (in units of the chemical potential), where q is the charge of
the spinor, and n is a non-negative integer that labels the Fermi surfaces.
Much as for holographic Fermi surfaces based on the Reissner-Nordstrom-AdS_5
solution, the dispersion relation of the excitations near the Fermi surface is
determined by the geometry close to the horizon, and one can obtain Fermi
liquid, marginal Fermi liquid, and non-Fermi liquid behaviors depending on the
value of k_F.
