Journal
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volume 327, Issue 2, Pages 603-641Publisher
SPRINGER
DOI: 10.1007/s00220-014-1954-8
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Funding
- A. von Humboldt Stiftung
- European Union [269217]
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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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