Just Renormalizable TGFT’s on U(1)d with Gauge Invariance

@article{Samary2012JustRT,
  title={Just Renormalizable TGFT’s on U(1)d with Gauge Invariance},
  author={Dine Ousmane Samary and Fabien Vignes-Tourneret},
  journal={Communications in Mathematical Physics},
  year={2012},
  volume={329},
  pages={545-578}
}
We study the polynomial Abelian or U(1)d Tensorial Group Field Theories equipped with a gauge invariance condition in any dimension d. We prove the just renormalizability at all orders of perturbation of the $${\varphi^4_6}$$φ64 and $${\varphi^6_5}$$φ56 random tensor models. We also deduce that the $${\varphi^4_5}$$φ54 tensor model is super-renormalizable. 
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