Exact Greenʼs function and Fermi surfaces from conformal gravity

We study the Dirac equation of a charged massless spinor on the general charged AdS black hole of conformal gravity. The equation can be solved exactly in terms of Heunʼs functions. We obtain the exact Greenʼs function in the phase space (ω,k). This allows us to obtain Fermi surfaces for both Fermi and non-Fermi liquids. Our analytic results provide a more elegant approach of studying some strongly interacting fermionic systems not only at zero temperature, but also at any finite temperature. At zero temperature, we analyse the motion of the poles in the complex ω plane and obtain the leading order terms of the dispersion relation, expressed as the Laurent expansion of ω in terms of k. We illustrate new distinguishing features arising at the finite temperature. The Greenʼs function with vanishing ω at finite temperature has a fascinating rich structure of spiked maxima in the plane of k and the fermion charge q.