Communications in Mathematical Physics

, Volume 366, Issue 2, pp 567–646 | Cite as

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

  • V. Rivasseau
  • F. Vignes-TourneretEmail author


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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Authors and Affiliations

  1. 1.Laboratoire de Physique Théorique, CNRS UMR 8627Université Paris SudOrsay CedexFrance
  2. 2.Institut Camille Jordan, CNRS UMR 5208Univ Lyon, Université Claude Bernard Lyon 1VilleurbanneFrance

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