  We numerically study the phase diagram of bosons tightly trapped in the
lowest band of an optical lattice and dispersively coupled to a single-mode
cavity field. The dynamics is encompassed by an extended Bose-Hubbard model.
Here, the cavity-mediated interactions are described by a two-body potential
term with a global range and by a correlated tunneling term where the hopping
amplitude depends on a global observable. We determine the ground state
properties in one dimension by means of the density matrix renormalization
group algorithm, focusing on the effects due to the correlated tunneling. The
latter is responsible for the onset of bond orders, manifesting in one
insulating and two gapless bond ordered phases. We discuss the resulting phases
for different geometries that correspond to different relative strengths of the
correlated tunneling coefficient. We finally analyze the scaling of the
entanglement entropy in the gapless bond ordered phases that appear entirely
due to global interactions and determine the corresponding central charges.
