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

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.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-000F-E561-E Version Permalink: http://hdl.handle.net/11858/00-001M-0000-001A-2356-1
Genre: Journal Article

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1207.6734 (Preprint), 485KB
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 Creators:
Carrozza, Sylvain1, Author              
Oriti, Daniele1, Author              
Rivasseau, Vincent, Author
Affiliations:
1Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_67201              

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Free keywords: High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc
 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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 Dates: 2012-07-2820132014
 Publication Status: Published in print
 Pages: 33 pages, 8 figures, 1 appendix
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 Rev. Method: -
 Identifiers: arXiv: 1207.6734
DOI: 10.1007/s00220-014-1954-8
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Title: Communications in Mathematical Physics
Source Genre: Journal
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Pages: - Volume / Issue: 327 (2) Sequence Number: - Start / End Page: 603 - 641 Identifier: -