  We study hard dimers on dynamical lattices in arbitrary dimensions using a
random tensor model. The set of lattices corresponds to triangulations of the
d-sphere and is selected by the large N limit. For small enough dimer
activities, the critical behavior of the continuum limit is the one of pure
random lattices. We find a negative critical activity where the universality
class is changed as dimers become critical, in a very similar way hard dimers
exhibit a Yang-Lee singularity on planar dynamical graphs. Critical exponents
are calculated exactly. An alternative description as a system of
`color-sensitive hard-core dimers' on random branched polymers is provided.
