  Excitations which carry "fractional" quantum numbers are known to exist in
one dimension in polyacetylene, and in two dimensions, in the fractional
quantum Hall effect. Fractional excitations have also been invoked to explain
the breakdown of the conventional theory of metals in a wide range of
three-dimensional materials. However the existence of fractional excitations in
three dimensions remains highly controversial. In this Letter we report direct
numerical evidence for the existence of a quantum liquid phase supporting
fractional excitations in a concrete, three-dimensional microscopic model - the
quantum dimer model on a diamond lattice. We demonstrate explicitly that the
energy cost of separating fractional monomer excitations vanishes in this
liquid phase, and that its energy spectrum matches that of the Coulomb phase in
(3+1) dimensional quantum electrodynamics.
