Fermi Surfaces and Analytic Green's Functions from Conformal Gravity

TL;DR

This paper constructs charged AdS black holes in conformal gravity, derives their Green's functions analytically, and explores Fermi surfaces, revealing differences between extremal and non-extremal cases.

Contribution

It provides the first analytic Green's functions for charged black holes in conformal gravity, including the effects of massive spin-2 hair.

Findings

Green's functions expressed in terms of Heun's functions

Identification of Fermi surfaces for non-Fermi liquids

Differences in Green's functions between extremal and non-extremal black holes

Abstract

We construct T^2-symmetric charged AdS black holes in conformal gravity. The most general solution up to an overall conformal factor contains three non-trivial parameters: the mass, electric charge and a quantity that can be identified as the massive spin-2 hair. We study the Dirac equation for the charged massless spinor in this background. The equation can be solved in terms of the general Heun's function for generic frequency \omega and wave number k. This allows us to obtain the analytic Green's function G(\omega, k) for both extremal and non-extremal black holes. For some special choice of back hole parameters, we find that the Green's function reduces to simpler hypergeometric or confluent hypergeometric functions. We study the Fermi surfaces associated with the poles of the Green's function with vanishing \omega. We find examples where the Fermi surfaces for non-Fermi liquids as well as the characteristic Fermi ones can arise. We illustrate the non-trivial differences in the Green's function and Fermi surfaces between the extremal and non-extremal black holes.