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arXiv · 1207.6734

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

Sylvain Carrozza·Daniele Oriti·Vincent Rivasseau
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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.

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Sylvain Carrozza, Daniele Oriti, Vincent Rivasseau. 2014-04-03. Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions. https://doi.org/10.1007/s00220-014-1954-8

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