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

Abstract

We study the polynomial Abelian or U(1)^d Tensorial Group Field Theories equipped with a gauge invariance condition in any dimension d. From our analysis, we prove the just renormalizability at all orders of perturbation of the phi^4_6 and phi^6_5 random tensor models. We also deduce that the phi^4_5 tensor model is super-renormalizable.

arXiv comment33 pages, 22 figures. One added paragraph on the different notions of connectedness, preciser formulation of the proof of the power counting theorem, more general statements about traciality of tensor graphs

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