Algebraic charge liquids

High-temperature superconductivity emerges in the copper oxide compounds on changing the electron density of an insulator in which the electron spins are antiferromagnetically ordered. A key characteristic of the superconductor(1) is that electrons can be extracted from it at zero energy only if their momenta take one of four specific values (the 'nodal points'). A central enigma has been the evolution of those zero-energy electrons in the metallic state between the antiferromagnet and the superconductor, and recent experiments yield apparently contradictory results. The oscillation of the resistance in this metal as a function of magnetic field(2,3) indicates that the zero-energy electrons carry momenta that lie on elliptical 'Fermi pockets', whereas ejection of electrons by high-intensity light indicates that the zero-energy electrons have momenta only along arc-like regions(4,5), or 'Fermi arcs'. We present a theory of new states of matter, which we call 'algebraic charge liquids', and which arise naturally between the antiferromagnet and the superconductor, and reconcile these observations. Our theory also explains a puzzling dependence of the density of superconducting electrons on the total electron density, and makes a number of unique predictions for future experiments.