  In this paper we analyze a quartic tensor model with one interaction for a
tensor of arbitrary rank. This model has a critical point where a continuous
limit of infinitely refined random geometries is reached. We show that the
critical point corresponds to a phase transition in the tensor model associated
to a breaking of the unitary symmetry. We analyze the model in the two phases
and prove that, in a double scaling limit, the symmetric phase corresponds to a
theory of infinitely refined random surfaces, while the broken phase
corresponds to a theory of infinitely refined random nodal surfaces. At leading
order in the double scaling limit planar surfaces dominate in the symmetric
phase, and planar nodal surfaces dominate in the broken phase.
