Symmetry breaking in tensor models

Understand

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.