Analytic fermionic Green's functions from holography

We find an analytically solvable model that captures essential features of the holographic Fermi surfaces. Both the Fermi momentum and the Green's function near the Fermi surface are analytically obtained. The geometry 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 IR geometry of this extremal two-charge black hole is conformal to AdS$_2 \times R^3$. 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.