Gauge theory for the cuprates near optimal doping

We describe the phase diagram of a 2+1-dimensional SU(2) gauge theory of fluctuating incommensurate spin density waves for the hole-doped cuprates. Our primary assumption is that all low-energy fermionic excitations are gauge neutral and electron-like, while the spin density wave order is fractionalized into Higgs fields transforming as adjoints of the gauge SU(2). The confining phase of the gauge theory is a conventional Fermi liquid with a large Fermi surface (and its associated d-wave superconductor). There is a quantum phase transition to a Higgs phase describing the "pseudogap" at lower doping. Depending on the quartic terms in the Higgs potential, the Higgs phase exhibits one or more of charge density wave, Ising-nematic, time-reversal odd scalar spin chirality, and Z(2) topological orders. It is notable that the emergent broken symmetries in our theory of fluctuating spin density waves coincide with those observed in diverse experiments. For the electron-doped cuprates, the spin density wave fluctuations are at wave vector (pi, pi), and then the corresponding SU(2) gauge theory only has a crossover between the confining and Higgs regimes, with an exponentially large confinement scale deep in the Higgs regime. On the Higgs side, for both the electron- and hole-doped cases, and at scales shorter than the confinement scale (which can be infinite when Z(2) topological order is present), the electron spectral function has a "fractionalized Fermi liquid" form with small Fermi surfaces. We also describe the deconfined quantum criticality of the Higgs transition in the limit of a large number of Higgs flavors, and perturbatively discuss its coupling to fermionic excitations.