Functional Renormalization Group analysis of a Tensorial Group Field Theory on $\mathbb{R}^3$
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We study a model of Tensorial Group Field Theory (TGFT) on R 3 from the point of view of the Functional Renormalization Group (FRG). This is the first attempt to apply a renormalization procedure to a TGFT model defined over a non-compact group manifold. IR divergences (with respect to the metric on R ) coming from the non-compactness of the group are regularised via compactification, and a thermodynamic limit is then taken. We identify then IR and UV fixed points of the RG flow and find strong hints of a phase transition of the TGFT system from a symmetric to a broken or condensate phase in the IR.
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In quantum optics, non-Fock coherent states with an infinite number of (soft) photons can be described in terms of a classical radiation field.
“since in the context of quantum optics it was understood that such non-Fock coherent states with an infinite number of (soft) photons can be described in terms of a classical radiation field [35].”
From Impact of nonlinear effective interactions on group field theory quantum gravity condensates (2016) · cites this paper as [35]
The unboundedness of L leads to a finite particle density in the infinite volume in contrast to a vanishing particle density for bounded L in the same limit.
“Furthermore, one can show that the unboundedness of L leads to a finite particle density in the infinite volume in contrast to a vanishing particle density for bounded L in the same limit [35].”
From Impact of nonlinear effective interactions on group field theory quantum gravity condensates (2016) · cites this paper as [35]
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- Authors
- Ben Geloun, J., Martini, R., & Oriti, D.
- Affiliations
- Max Planck Institute for Gravitational Physics (DE)
- Max Planck Society (DE)
- Venue
- EPL (Europhysics Letters)
- Publisher
- IOP Publishing
- Published
- 2015-11-17
- Volume
- 112
- Issue
- 3
- Pages
- 31001
- ISSN
- 0295-5075 (ISSN-L)
- 1286-4854
- OpenAlex
- W1896803414
- Cited by
- 62
- References
- 58
- Citations by year
- 2026: 3 · 2025: 1 · 2024: 5 · 2023: 3 · 2022: 2 · 2021: 6 · 2020: 9 · 2019: 7 · 2018: 10 · 2017: 5 · 2016: 11
- FWCI
- 5.46
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Europhysics Letters (EPL) (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Archivio istituzionale della ricerca (Alma Mater Studiorum Università di Bologna) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Physical Sciences › Mathematics › Mathematical Physics › advanced mathematical theories
- Keywords
- tensorial group field theory, functional renormalization group, three-dimensional space, infrared divergences, compactification, thermodynamic limit, infrared fixed point, ultraviolet fixed point, phase transitions, condensation, quantum gravity
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