Renormalization of 3d quantum gravity from matrix models
Open accessAbstract
Lorentzian simplicial quantum gravity is a non-perturbatively defined theory of quantum gravity which predicts a positive cosmological constant. Since the approach is based on a sum over space–time histories, it is perturbatively non-renormalizable even in three dimensions. By mapping the three-dimensional theory to a two-matrix model with ABAB interaction we show that both the cosmological and the (perturbatively) non-renormalizable gravitational coupling constant undergo additive renormalizations consistent with canonical quantization.
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The Lorentzian dynamical triangulation model can be translated into a two-matrix model, the ABAB model; Feynman diagrams correspond to dual graphs of a triangulation, and matrix model amplitudes become particular sums of transfer matrix elements.
“The Lorentzian dynamical triangulation model can also be translated into a two-matrix model, the so-called ABAB model. The Feynman diagrams of the matrix model correspond to dual graphs of a triangulation, and matrix model amplitudes become particular sums of transfer matrix elements in the gravitational theory [11, 14, 15].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [14]
The matrix model connection can be used to show that Newton's constant and the cosmological constant are additively renormalized, and to analyze the apparent nonrenormalizability of ordinary field theoretical approach.
“For example, the matrix model connection can be used to show that Newton’s constant and the cosmological constant are additively renormalized [14], and to analyze the apparent nonrenormalizability of ordinary field theoretical approach.”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [14]
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2 + 1 dimensional gravity as an exactly soluble system
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Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe
Carlip, S. (2005) · Living Reviews in Relativity · doi:10.12942/lrr-2005-1 · Cited by 172 · see citing works
- Authors
- Ambjørn, J., Jurkiewicz, J., & Loll, R.
- Affiliations
- Jagiellonian University (PL)
- Utrecht University (NL)
- Corresponding author
- Jurkiewicz, J.
- Loll, R.
- Venue
- Physics Letters B
- Publisher
- Elsevier BV
- Published
- 2004-02
- Volume
- 581
- Issue
- 3-4
- Pages
- 255-262
- ISSN
- 0370-2693 (ISSN-L)
- OpenAlex
- W2005252752
- Cited by
- 29
- References
- 1
- Citations by year
- 2023: 1 · 2022: 1 · 2021: 3 · 2020: 2 · 2019: 1 · 2016: 2 · 2013: 1 · 2012: 3
- FWCI
- 1.58
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Physics Letters B (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Utrecht University Repository (Utrecht University) (submittedVersion, other-oa)
- Research at the University of Copenhagen (University of Copenhagen) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- three-dimensional quantum gravity, matrix models, two-matrix model, renormalization, cosmological constant, canonical quantization, gravitational coupling constant
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