Bekenstein-hawking entropy and strange metals

Abstract

We examine models of fermions with infinite-range interactions that realize non-Fermi liquids with a continuously variable U(1) charge density Q and a nonzero entropy density S at vanishing temperature. Real-time correlators of operators carrying U(1) charge q at a low temperature T are characterized by a Q-dependent frequency ωS=(qT/h{stroke}(∂S/∂Q)which determines a spectral asymmetry. We show that the correlators match precisely with those of the two-dimensional anti-de Sitter (AdS2) horizons of extremal charged black holes. On the black hole side, the matching employs S as the Bekenstein-Hawking entropy density and the laws of black hole thermodynamics that relate ∂S/∂Q/(2π) to the electric field strength in AdS2. The fermion model entropy is computed using the microscopic degrees of freedom of a UV complete theory without supersymmetry.