Communications in Mathematical Physics

, Volume 345, Issue 2, pp 477–506 | Cite as

Constructive Tensor Field Theory: the \({T^4_3}\) Model



We build constructively the simplest tensor field theory which requires some renormalization, namely the rank three tensor theory with quartic interactions and propagator inverse of the Laplacian on \({U(1)^3}\). This superrenormalizable tensor field theory has a power counting almost similar to ordinary \({\phi^4_2}\). Our construction uses the multiscale loop vertex expansion (MLVE) recently introduced in the context of an analogous vector model. However, to prove analyticity and Borel summability of this model requires new estimates on the intermediate field integration, which is now of matrix rather than of scalar type.


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© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Laboratoire de Physique Théorique, CNRS UMR 8627Université Paris SudOrsay CedexFrance
  2. 2.Centre de Physique Théorique, CNRS UMR 7644École PolytechniquePalaiseau CedexFrance
  3. 3.Perimeter Institute for Theoretical PhysicsWaterlooCanada

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