  We derive an extended lattice gauge theory type action for quantum dimer
models and relate it to the height representations of these systems. We examine
the system in two and three dimensions and analyze the phase structure in terms
of effective theories and duality arguments. For the two-dimensional case we
derive the effective potential both at zero and finite temperature. The
zero-temperature theory at the Rokhsar-Kivelson (RK) point has a critical point
related to the self-dual point of a class of $Z_N$ models in the $N\to\infty$
limit. Two phase transitions featuring a fixed line are shown to appear in the
phase diagram, one at zero temperature and at the RK point and another one at
finite temperature above the RK point. The latter will be shown to correspond
to a Kosterlitz-Thouless (KT) phase transition, while the former will be
governed by a KT-like universality class, i.e., sharing many features with a KT
transition but actually corresponding to a different universality class. On the
other hand, we show that at the RK point no phase transition happens at finite
temperature. For the three-dimensional case we derive the corresponding dual
gauge theory model at the RK point. We show in this case that at zero
temperature a first-order phase transition occurs, while at finite temperatures
both first- and second-order phase transitions are possible, depending on the
relative values of the couplings involved.
