Bekenstein-Hawking Entropy and Strange Metals

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 ω_S=(q T /ℏ)(∂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 )/(2 π ) 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.