  A long standing problem in the study of the under-hole-doped cuprates has
been the description of the Fermi surfaces underlying the high magnetic field
quantum oscillations, and their connection to the higher temperature pseudogap
metal. Harrison and Sebastian (arXiv:1103.4181) proposed that the pseudogap
`Fermi arcs' are reconstructed into an electron pocket by field-induced charge
density wave order. But computations on such a model (Zhang and Mei,
arXiv:1411.2098) show an unobserved additional oscillation frequency from a
Fermi surface arising from the backsides of the hole pockets completing the
Fermi arcs. We describe a transition from a fractionalized Fermi liquid (FL*)
model of the pseudogap metal, to a metal with bi-directional charge density
wave order without fractionalization. We show that the confinement of the
fermionic spinon excitations of the FL* across this transition can eliminate
the unobserved oscillation frequency.
