  In the conventional theory of density wave ordering in metals, the onset of
spin density wave (SDW) order co-incides with the reconstruction of the Fermi
surfaces into small 'pockets'. We present models which display this transition,
while also displaying an alternative route between these phases via an
intermediate phase with topological order, no broken symmetry, and pocket Fermi
surfaces. The models involve coupling emergent gauge fields to a fractionalized
SDW order, but retain the canonical electron operator in the underlying
Hamiltonian. We establish an intimate connection between the suppression of
certain defects in the SDW order, and the presence of Fermi surface sizes
distinct from the Luttinger value in Fermi liquids. We discuss the relevance of
such models to the physics of the hole-doped cuprates near optimal doping.
