Gauge theory for the cuprates near optimal doping*

We propose a SU(2) gauge theory with fermionic low-energy excitations as an effective field theory for the cuprate high-temperature superconductors. For the hole-doped compounds, the theory describes fluctuating incommensurate spin-density waves. While we recover the conventional Fermi-liquid state as the confining phase of the theory at large doping, there is a quantum phase transition to a Higgs phase corresponding to the pseudogap at low doping. Depending on details of the theory, the Higgs phase shows one or more of charge-density wave, Ising-nematic, scalar spin chirality, and Z₂ topological order. For the electron-doped systems, we assume commensurate spin-density wave fluctuations and there is only a crossover between the confining and the Higgs regime, with an exponentially large confinement length deep in the Higgs regime. For both the electron- and hole-doped systems, the electronic spectral function shows small Fermi surfaces at scales shorter than the confinement length. Finally, we present a large-N analysis of the deconfined quantum criticality of the Higgs transition.