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We show that there are two types of RVB liquid phases present inthree-dimensional quantum dimer models, corresponding to the deconfining phasesof U(1) and Z_2 gauge theories in d=3+1. The former is found on the bipartitecubic lattice and is the generalization of the critical point in the squarelattice quantum dimer model found originally by Rokhsar and Kivelson. Thelatter exists on the non-bipartite face-centred cubic lattice and generalizesthe RVB phase found earlier by us on the triangular lattice. We discuss theexcitation spectrum and the nature of the ordering in both cases. Both phasesexhibit gapped spinons. In the U(1) case we find a collective, linearlydispersing, transverse excitation, which is the photon of the low energyMaxwell Lagrangian and we identify the ordering as quantum order in Wen'ssense. In the Z_2 case all collective excitations are gapped and, as in d=2,the low energy description of this topologically ordered state is the purelytopological BF action. As a byproduct of this analysis, we unearth a furthergapless excitation, the pi0n, in the square lattice quantum dimer model at itscritical point.Comment: 9 pages, 2 figure

Three-dimensional resonating-valence-bond liquids and their excitations