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Parametric Representation of Rank d Tensorial Group Field Theory: Abelian Models with Kinetic Term sum_s|p_s| + \mu

Ben Geloun, J., & Toriumi, R. (2015). Parametric Representation of Rank d Tensorial Group Field Theory: Abelian Models with Kinetic Term sum_s|p_s| + \mu. Journal of Mathematical Physics, 56: 093503. doi:10.1063/1.4929771.

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### Creators

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Creators:
Ben Geloun, Joseph1, Author
Toriumi, Reiko, Author
Affiliations:
1Quantum Gravity and Unified Theorie, ou_24014

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Free keywords: High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP
Abstract: We consider the parametric representation of the amplitudes of Abelian models in the so-called framework of rank $d$ Tensorial Group Field Theory. These models are called Abelian because their fields live on $U(1)^D$. We concentrate on the case when these models are endowed with particular kinetic terms involving a linear power in momenta. New dimensional regularization and renormalization schemes are introduced for particular models in this class: a rank 3 tensor model, an infinite tower of matrix models $\phi^{2n}$ over $U(1)$, and a matrix model over $U(1)^2$. For all divergent amplitudes, we identify a domain of meromorphicity in a strip determined by the real part of the group dimension $D$. From this point, the ordinary subtraction program is applied and leads to convergent and analytic renormalized integrals. Furthermore, we identify and study in depth the Symanzik polynomials provided by the parametric amplitudes of generic rank $d$ Abelian models. We find that these polynomials do not satisfy the ordinary Tutte's rules (contraction/deletion). By scrutinizing the "face"-structure of these polynomials, we find a generalized polynomial which turns out to be stable only under contraction.

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Dates: 2014-09-0120152015
Publication Status: Published in print
Pages: 69 pages, 35 figures
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Rev. Method: -
Identifiers: arXiv: 1409.0398
DOI: 10.1063/1.4929771
Degree: -

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Title: Journal of Mathematical Physics
Source Genre: Journal
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Publ. Info: Woodbury, N.Y. [etc.] : American Institute of Physics
Pages: - Volume / Issue: 56 Sequence Number: 093503 Start / End Page: - Identifier: ISSN: 0022-2488
CoNE: https://pure.mpg.de/cone/journals/resource/954922836227