Communications in Mathematical Physics

, Volume 327, Issue 2, pp 603–641 | Cite as

Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions

  • Sylvain CarrozzaEmail author
  • Daniele Oriti
  • Vincent Rivasseau


We tackle the issue of renormalizability for Tensorial Group Field Theories (TGFT) including gauge invariance conditions, with the rigorous tool of multi-scale analysis, to prepare the ground for applications to quantum gravity models. In the process, we define the appropriate generalization of some key QFT notions, including connectedness, locality and contraction of (high) subgraphs. We also define a new notion of Wick ordering, corresponding to the subtraction of (maximal) melonic tadpoles. We then consider the simplest examples of dynamical 4-dimensional TGFT with gauge invariance conditions for the Abelian U(1) case. We prove that they are super-renormalizable for any polynomial interaction.


Quantum Gravity Lattice Gauge Theory Tensor Model Feynman Amplitude Spin Foam Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Sylvain Carrozza
    • 1
    • 2
    Email author
  • Daniele Oriti
    • 2
  • Vincent Rivasseau
    • 1
  1. 1.Laboratoire de Physique Théorique, CNRS UMR 8627Université Paris XIOrsay CedexFrance
  2. 2.Max Planck Institute for Gravitational Physics, Albert Einstein InstituteGolmGermany

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