Abstract
Generalizing matrix models, tensor models generate dynamical triangulations in any dimension and support a 1/N expansion. Using the intermediate field representation we explicitly rewrite a quartic tensor model as a field theory for a fluctuation field around a vacuum state corresponding to the resummation of the entire leading order in 1/N (a resummation of the melonic family). We then prove that the critical regime in which the continuum limit in the sense of dynamical triangulations is reached is precisely a phase transition in the field theory sense for the fluctuation field.
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Delepouve, T., Gurau, R. Phase transition in tensor models. J. High Energ. Phys. 2015, 178 (2015). https://doi.org/10.1007/JHEP06(2015)178
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DOI: https://doi.org/10.1007/JHEP06(2015)178