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  Functional Renormalisation Group Approach for Tensorial Group Field Theory: a Rank-3 Model

Benedetti, D., Geloun, J. B., & Oriti, D. (2015). Functional Renormalisation Group Approach for Tensorial Group Field Theory: a Rank-3 Model. Journal of high energy physics: JHEP, 2015(03): 084. Retrieved from http://arxiv.org/abs/1411.3180.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0024-4266-D Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0026-BA38-E
Genre: Journal Article

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 Creators:
Benedetti, Dario1, Author              
Geloun, Joseph Ben, Author
Oriti, Daniele1, Author              
Affiliations:
1Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:67201              

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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 set up the Functional Renormalisation Group formalism for Tensorial Group Field Theory in full generality. We then apply it to a rank-3 model over U(1) x U(1) x U(1), endowed with a linear kinetic term and nonlocal interactions. The system of FRG equations turns out to be non-autonomous in the RG flow parameter. This feature is explained by the existence of a hidden scale, the radius of the group manifold. We investigate in detail the opposite regimes of large cut-off (UV) and small cut-off (IR) of the FRG equations, where the system becomes autonomous, and we find, in both case, Gaussian and non-Gaussian fixed points. We derive and interpret the critical exponents and flow diagrams associated with these fixed points, and discuss how the UV and IR regimes are matched at finite N. Finally, we discuss the evidence for a phase transition from a symmetric phase to a broken or condensed phase, from an RG perspective, finding that this seems to exist only in the approximate regime of very large radius of the group manifold, as to be expected for systems on compact manifolds.

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 Dates: 2014-11-122015
 Publication Status: Published in print
 Pages: 28 pages, 14 figures
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1411.3180
URI: http://arxiv.org/abs/1411.3180
 Degree: -

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Title: Journal of high energy physics : JHEP
Source Genre: Journal
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Publ. Info: Bologna, Italy : Società italiana di fisica
Pages: - Volume / Issue: 2015 (03) Sequence Number: 084 Start / End Page: - Identifier: ISSN: 1126-6708
CoNE: http://pubman.mpdl.mpg.de/cone/journals/resource/111021927548002