Fermi Surfaces And Analytic Green’s Functions From Confor-Mal Gravity

Gravity/gauge duality (AdS/CFT) is one of the most far-reaching physical idea in recent years, it is a strong/weak duality, which makes it possible to study strongly coupled field theory through weak gravity,therefore this duality is widely used in studying strongly correlated systems in condensed matter physics in re-cent years. This thesis use Gravity/gauge duality to investigate strongly coupled fermion systems at finite charge density. The weak gravity that the previous s-tudies usually chose are Einstein gravity or it minimally coupled vector field. In this case, it’s often hard to solve the Dirac equation analytically, which brings us much inconvenience to investigate the physical properties of the fermion sys-tems further. This thesis instead chooses conformal gravity, We first construct T2-symmetric charged AdS black holes of conformal gravity. The most general so-lution up to an overall conformal factor contains three non-trivial parameters:the mass, the electric charge and a quantity that can be identified as the massive spin-2hair. Then we classify the solution into the extremal and non-extremal solution. We study the Dirac equation for the charged massless fermion in these backgrounds. The equation can be solved in terms of the general Heun’s function for generic frequency and wave number. This allows us to obtain the analyt-ic Green’s function G(ω,k) for both extremal and non-extremal black holes. For some special choice of back hole parameters, it shows that the Green’s function re-duces to simpler hypergeometric or confluent hypergeometric functions. Through studying the poles of the Green’s function, the thesis shows the conditions under which the fermi surface will arise. The investigation of this thesis also illustrate the non-trivial differences in Fermi surfaces from the extremal and non-extremal black holes.