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Constructive Tensor Field Theory: The \({T_{4}^{4}}\) Model

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Abstract

We continue our constructive study of tensor field theory through the next natural model, namely the rank four tensor theory with quartic melonic interactions and propagator inverse of the Laplacian on U(1)4. This superrenormalizable tensor field theory has a power counting quite similar to ordinary \({\phi^4_3}\). We control the model via a multiscale loop vertex expansion which has to be pushed quite beyond the one of the \({T^{4}_{3}}\) model and we establish its Borel summability in the coupling constant. This paper is also a step to prepare the constructive treatment of just renormalizable models, such as the \({T^{4}_{5}}\) model with quartic melonic interactions.

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  1. Laboratoire de Physique Théorique, CNRS UMR 8627, Université Paris Sud, 91405, Orsay Cedex, France

    V. Rivasseau

  2. Institut Camille Jordan, CNRS UMR 5208, Univ Lyon, Université Claude Bernard Lyon 1, 69622, Villeurbanne, France

    F. Vignes-Tourneret

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Rivasseau, V., Vignes-Tourneret, F. Constructive Tensor Field Theory: The \({T_{4}^{4}}\) Model. Commun. Math. Phys. 366, 567–646 (2019). https://doi.org/10.1007/s00220-019-03369-9

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