  Nonlocal order parameters for deconfinement, such as the entanglement entropy
and Wilson loops, depend on spatial surfaces \Sigma. These observables are
given holographically by the area of a certain bulk spatial surface \Gamma,
ending on \Sigma. At finite charge density it is natural to consider the
electric flux through the bulk surface \Gamma, in addition to its area. We show
that this flux provides a refined order parameter that can distinguish
`fractionalized' phases, with charged horizons, from what we term `cohesive'
phases, with charged matter in the bulk. Fractionalization leads to a volume
law for the flux through the surface, the flux for deconfined but cohesive
phases is between a boundary and a volume law, while finite density confined
phases have vanishing flux through the surface. We suggest two possible field
theoretical interpretations for this order parameter. The first is as
information extracted from the large N reduced density matrix associated to
\Sigma. The second is as surface operators dual to polarized bulk `D-branes',
carrying an electric dipole moment.
