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We study the Dirac equation of a charged massless spinor on the generalcharged AdS black hole of conformal gravity. The equation can be solved exactlyin terms of Heun's functions. We obtain the exact Green's function in the phasespace (\omega,k). This allows us to obtain Fermi surfaces for both Fermi andnon-Fermi liquids. Our analytic results provide a more elegant approach ofstudying some strongly interacting fermionic systems not only at zerotemperature, but also at any finite temperature. At zero temperature, weanalyse the motion of the poles in the complex \omega plane and obtain theleading order terms of the dispersion relation, expressed as the Laurentexpansion of \omega in terms of k. We illustrate new distinguishing featuresarising at the finite temperature. The Green's function with vanishing \omegaat finite temperature has a fascinating rich structure of spiked maxima in theplane of k and the fermion charge q.

Exact Green's Function and Fermi Surfaces from Conformal Gravity