Nonperturbative summation over 3D discrete topologies
Open accessAbstract
The group field theories realizing the sum over all triangulations of all topologies of 3D discrete gravity amplitudes are known to be nonuniquely Borel summable. We modify these models to construct a new group field theory which is proved to be uniquely Borel summable, defining in an unambiguous way a nonperturbative sum over topologies in the context of 3D dynamical triangulations and spin foam models. Moreover, we give some arguments to support the fact that, despite our modification, this new model is similar to the original one, and therefore could be taken as a definition of the sum over topologies of 3D quantum gravity amplitudes.
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Recent work has suggested a method for summing over all topologies in spin foam models, allowing quantum fluctuations of spacetime topology.
“While spin foam models ordinarily assume a fixed spacetime topology, recent work has suggested a method for summing over all topologies as well, thus allowing quantum fluctuations of spacetime topology [132].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [132]
Freidel and Loupre considered a variant of the Ponzano-Regge model and showed that although the sum over topologies diverges, it is Borel summable.
“Building on work by Boulatov [60], Freidel and Loupre have recently considered a variant of the Ponzano-Regge model, and have shown that although the sum over topologies diverges, it is Borel summable [132].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [132]
The model considered by Freidel and Loupre is not exactly the Ponzano-Regge model, and it is not clear that it is ordinary quantum gravity.
“The model considered in [132] is not exactly the Ponzano-Regge model, and it is not clear that it is really “ordinary” quantum gravity.”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [132]
Freidel and Louapre demonstrated that such re-summing is possible for some three-dimensional group field theories.
“Freidel and Louapre [187] have shown that this is indeed possible for certain GFT’s in three dimensions.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [187]
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- Authors
- Freidel, L., & Louapre, D.
- Affiliations
- École Normale Supérieure de Lyon (FR)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2003-11-06
- Volume
- 68
- Issue
- 10
- ISSN
- 0556-2821 (ISSN-L)
- 1089-4918
- OpenAlex
- W2010204621
- Cited by
- 80
- References
- 22
- Citations by year
- 2025: 1 · 2023: 1 · 2021: 29 · 2019: 1 · 2018: 1 · 2016: 2 · 2013: 4 · 2012: 6
- FWCI
- 2.99
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- group field theory, Borel summability, three-dimensional quantum gravity, dynamical triangulations, spin foam models, discrete gravity
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