2012/07/31 by Sylvain Carrozza, Daniele Oriti, Vincent Rivasseau · 1 citation
Physics and Astronomy · #hep-th #gr-qc
paper · pdf · doi:10.1007/s00220-014-1954-8
published as Commun. Math. Phys. 327, 603-641 (2014) · 33 pages, 8 figures, 1 appendix. v2: minor corrections and improvements. v3: minor modifications to match published version
arxiv created 2014/04/03 · arxiv updated 2014/04/04
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.