  Recent experiments in the underdoped regime of the hole-doped cuprates have
found evidence for an incommensurate charge density wave state. We present an
analysis of the charge ordering instabilities in a metal with antiferromagnetic
correlations, where the electronic excitations are coupled to the
fractionalized excitations of a quantum fluctuating antiferromagnet on the
square lattice. The resulting charge density wave state emerging out of such a
fractionalized Fermi-liquid (FL*) has wavevectors of the form $(\pm Q_0,0),
(0,\pm Q_0)$, with a predominantly $d$-form factor, in agreement with
experiments on a number of different families of the cuprates. In contrast, as
previously shown, the charge density wave instability of a nearly
antiferromagnetic metal with a large Fermi surface, interacting via short-range
interactions, has wavevectors of the type $(\pm Q_0,\pm Q_0)$. Our results show
that the observed charge density wave appears as a low-energy instability of a
fractionalized metallic state linked to the proximity to an antiferromagnetic
insulator, and the pseudogap regime can be described by such a metal at least
over intermediate length and energy scales.
