Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2012

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

Abstract

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.

Dates and versions

hal-00722545 , version 1 (02-08-2012)

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Sylvain Carrozza, Daniele Oriti, Vincent Rivasseau. Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions. 2012. ⟨hal-00722545⟩
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