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Symmetry breaking in tensor models

Dario Benedetti*

Razvan Gurau†

  • Laboratoire de Physique Théorique, CNRS-UMR 8627, Université Paris-Sud 11, 91405 Orsay Cedex, France

  • Centre de Physique Théorique, CNRS UMR 7644, École Polytechnique, 91128 Palaiseau Cedex, France and Perimeter Institute for Theoretical Physics, 31 Caroline Street North, N2L 2Y5, Waterloo, Ontario, Canada

  • *dario.benedetti@th.u-psud.fr
  • †rgurau@cpht.polytechnique.fr
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Phys. Rev. D 92, 104041 – Published 23 November, 2015

DOI: https://doi.org/10.1103/PhysRevD.92.104041

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.

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Phys. Rev. D 92, 104041– Published 23 November, 2015
  • Received 8 July 2015

© 2015 American Physical Society

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