Functional renormalization group analysis of tensorial group field theories onRd
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Rank-$d$ tensorial group field theories are quantum field theories (QFTs) defined on a group manifold ${G}^{\ifmmode\times\else\texttimes\fi{}d}$, which represent a nonlocal generalization of standard QFT and a candidate formalism for quantum gravity, since, when endowed with appropriate data, they can be interpreted as defining a field theoretic description of the fundamental building blocks of quantum spacetime. Their renormalization analysis is crucial both for establishing their consistency as quantum field theories and for studying the emergence of continuum spacetime and geometry from them. In this paper, we study the renormalization group flow of two simple classes of tensorial group field theories (TGFTs), defined for the group $G=\mathbb{R}$ for arbitrary rank, both without and with gauge invariance conditions, by means of functional renormalization group techniques. The issue of IR divergences is tackled by the definition of a proper thermodynamic limit for TGFTs. We map the phase diagram of such models, in a simple truncation, and identify both UV and IR fixed points of the RG flow. Encouragingly, for all the models we study, we find evidence for the existence of a phase transition of condensation type.
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The results support the idea proposed in Ref. [36] that the Laplacian in the kinetic operator K might only be a property of the UV completed GFT without a significant physical effect in the effectively continuous region.
“The results of this article can also be seen as a support of the idea proposed in Ref. [36]: The Laplacian in the kinetic operator K , originally motivated by field theoretic arguments to guarantee the consistent implementation of a renormalization scheme, might only be a property of the UV completed GFT without a significant physical effect in the effectively continuous region”
From Impact of nonlinear effective interactions on group field theory quantum gravity condensates (2016) · cites this paper as [36]
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Renormalization of a tensorial field theory on the homogeneous space SU(2)/U(1)Preprint
Lahoche, V., & Oriti, D. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1506.08393 · Cited by 16 · see citing works
Self-citationEffective equations for GFT condensates from fidelityPreprint
Sindoni, L. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1408.3095 · Cited by 16 · see citing works
SCHWINGER-DYSON EQUATIONS IN GROUP FIELD THEORIES OF QUANTUM GRAVITY
Krajewski, T. (2013) · WORLD SCIENTIFIC eBooks · doi:10.1142/9789814518550_0050 · Cited by 15 · see citing works
B, J. M. A. (2017) · Advances in High Energy Physics · doi:10.1155/2017/4015145 · Cited by 10 · see citing works
Krajewski, T., & Toriumi, R. (2016) · HAL AMU · doi:10.1088/1751-8113/49/38/38540 · Cited by 8 · see citing works
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The nonperturbative functional renormalization group and its applications
Dupuis, N., Canet, L., Eichhorn, A., Metzner, W., Pawlowski, J. M., Tissier, M., & Wschebor, N. (2021) · Physics Reports · doi:10.1016/j.physrep.2021.01.001 · Cited by 660 · see citing works
de Cesare, M., Pithis, A. G. A., & Sakellariadou, M. (2016) · Physical Review D · doi:10.1103/physrevd.94.064051 · Cited by 72 · see citing works
Impact of nonlinear effective interactions on group field theory quantum gravity condensates
Pithis, A. G. A., Sakellariadou, M., & Tomov, P. (2016) · Physical Review D · doi:10.1103/physrevd.94.064056 · Cited by 34 · see citing works
- Authors
- Geloun, J. B., Martini, R., & Oriti, D.
- Affiliations
- UNESCO (FR)
- Max Planck Institute for Gravitational Physics (DE)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2016-07-06
- Volume
- 94
- Issue
- 2
- ISSN
- 2470-0010 (ISSN-L)
- 2470-0029
- OpenAlex
- W2262198343
- Cited by
- 71
- References
- 127
- Citations by year
- 2026: 3 · 2025: 2 · 2024: 7 · 2023: 3 · 2022: 3 · 2021: 9 · 2020: 8 · 2019: 7 · 2018: 12 · 2017: 8 · 2016: 9
- FWCI
- 6.80
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. D/Physical review. D. (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Max Planck Digital Library (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion, other-oa)
- Archivio istituzionale della ricerca (Alma Mater Studiorum Università di Bologna) (submittedVersion)
- arXiv (Cornell University)
- Funders
- John Templeton Foundation (ID44100)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Mathematics › Mathematical Physics › advanced mathematical theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- tensorial group field theory, functional renormalization group, renormalization group flow, quantum gravity, nonlocal quantum field theory, gauge invariance, infrared divergences, thermodynamic limit, phase diagram, ultraviolet fixed point, condensation phase transition, quantum spacetime
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
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