We present a theoretical framework for cuprate superconductors based on a fractionalized Fermi liquid (FL*) description of the intermediate-temperature pseudogap phase at low doping. In this picture, FL* theory predicts hole pockets with fractional area at hole doping $p$, in contrast to the larger pocket area expected from spin-density-wave theory. Magnetotransport experiments, including the observation of the Yamaji angle, provide strong evidence for hole-pocket quasiparticles that tunnel coherently between square-lattice layers, supporting the FL* scenario.

For a single-band model, the FL* phase can be formulated through a layer construction containing a pair of ancilla qubits on each site, known as the ancilla layer model (ALM). Its mean-field theory produces hole pockets of the expected area and reproduces the gapped anti-nodal photoemission spectrum across the Brillouin zone. Beyond mean field, fluctuations are captured by an SU(2) gauge theory built on a background spin liquid with critical Dirac spinons. Monte Carlo simulations of the thermal SU(2) gauge theory show that these hole pockets evolve into Fermi arcs in photoemission.

Upon lowering temperature, one possible route to confinement of the FL* state leads to a $d$-wave superconductor through a Kosterlitz-Thouless transition of vortices, yielding nodal Bogoliubov quasiparticles with anisotropic velocities and vortices surrounded by halos of charge order. A second route produces a charge-ordered metallic state with quantum oscillations consistent with experiment. In both cases, the confinement transitions are driven by condensation of an SU(2) fundamental Higgs field, which also offers a fractionalized description of intertwined orders.