Fractionalized Fermi liquids and the pseudogap

Fractionalized Fermi liquids (FL*) are metals with Fermi surfaces of electron-like quasiparticles; however the volume enclosed by the Fermi surface is not equal to the Luttinger value determined by the density of all electrons. There are general non-perturbative arguments that any such state with a non-Luttinger volume must also have emergent gauge excitations which have vanishing energy on manifolds of non-trivial topology. In doped antiferromagnets with hole density $p$, the Luttinger volume of a closed Fermi surface of holes is $1+p$ in the state without antiferromagnetic order. Simple FL* models of doped antiferromagnets will be described with ground states which preserve all symmetries, and have hole pockets of total volume $p$. Such models provide natural explanations for a number of recent observations on the pseudogap phase of the hole-doped cuprate superconductors. Confinement transitions of such FL* phases to conventional phases will also be described.