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

Sylvain Carrozza (1, 2) , Daniele Oriti (2) , Vincent Rivasseau (1)

1 LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]
2 AEI - Max Planck Institute for Gravitational Physics (Albert Einstein Institute)

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.

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]; Physique des Hautes Energies - Théorie [hep-th]

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