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Journal Article

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

MPS-Authors
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Carrozza,  Sylvain
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Oriti,  Daniele
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

1207.6734
(Preprint), 485KB

CMP327_603.pdf
(Any fulltext), 735KB

Supplementary Material (public)

carrozza103012.pdf
(Supplementary material), 953KB

Citation

Carrozza, S., Oriti, D., & Rivasseau, V. (2014). Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions. Communications in Mathematical Physics, 327(2), 603-641. doi:10.1007/s00220-014-1954-8.


Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-E561-E
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.