Symmetry breaking in tensor models

Abstract

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.

References in corpus (8)

• Random tensor models in the large N limit: Uncoloring the colored tensor models
• The topological structure of scaling limits of large planar maps
• The 1/N expansion of colored tensor models
• Enhancing non-melonic triangulations: A tensor model mixing melonic and planar maps
• Discrete Renormalization Group for SU(2) Tensorial Group Field Theory
• Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order
• An analysis of the intermediate field theory of $T^4$ tensor model
• Phase Transition in Tensor Models

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