Strings in less than one dimension
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The (p,q) minimal string was conjectured to be equivalent to a random matrix integral.
“For the particular case where the matter sector is the (p, q) minimal model, the resulting string model is called the (p, q) minimal string, which famously was conjectured to be equivalent to a random matrix integral, stemming from ideas around random triangulations of a 2d surface (Brezin and Kazakov 1990; Douglas and Shenker 1990; Gross and Migdal 1990).”
From Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity (2023) · cites this paper as Douglas and Shenker 1990
The number N of diff-inequivalent triangulations of a given four-dimensional manifold grows exponentially only with the number n of simplices; N(n) < exp{αn} for large n.
“The number N of diff-inequivalent triangulations of a given four dimensional manifold grows exponentially only with the number n of simplices [26]. That is N ( n ) < exp { αn } for large n .”
From Barrett–Crane model from a Boulatov–Ooguri field theory over a homogeneous space (2000) · cites this paper as [26]
Cites
Brézin, E., Itzykson, C., Parisi, G., & Zuber, J. B. (1978) · Communications in Mathematical Physics · doi:10.1007/bf01614153 · Cited by 1,479 · see citing works
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Intersection theory on the moduli space of curves and the matrix airy function
Kontsevich, M. (1992) · Communications in Mathematical Physics · doi:10.1007/bf02099526 · Cited by 1,472 · see citing works
2D gravity and random matrices
Francesco, P. D., Ginsparg, P., & Zinn-Justin, J. (1995) · Physics Reports · doi:10.1016/0370-1573(94)00084-g · Cited by 1,332 · see citing works
Barrett–Crane model from a Boulatov–Ooguri field theory over a homogeneous space
De Pietri, R., Freidel, L., Krasnov, K., & Rovelli, C. (2000) · Nuclear Physics B · doi:10.1016/s0550-3213(00)00005-5 · Cited by 244 · see citing works
Spacetime as a Feynman diagram: the connection formulation
Reisenberger, M. P., & Rovelli, C. (2001) · Classical and Quantum Gravity · doi:10.1088/0264-9381/18/1/308 · Cited by 202 · see citing works
Two-dimensional quantum gravity in Minkowski space
Banks, T., & O'Loughlin, M. (1991) · Nuclear Physics B · doi:10.1016/0550-3213(91)90547-b · Cited by 192 · see citing works
Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity
Mertens, T. G., & Turiaci, G. J. (2023) · Living Reviews in Relativity · doi:10.1007/s41114-023-00046-1 · Cited by 181 · see citing works
Liouville quantum gravity — holography, JT and matrices
Mertens, T. G., & Turiaci, G. J. (2021) · Journal of High Energy Physics · doi:10.1007/jhep01(2021)073 · Cited by 130 · see citing works
Simplicial quantum gravity in more than two dimensions
Godfrey, N., & Gross, M. (1991) · Physical Review D · doi:10.1103/physrevd.43.r1749 · Cited by 93 · see citing works
Ooguri, H. (1992) · Nuclear Physics B · doi:10.1016/0550-3213(92)90188-h · Cited by 76 · see citing works
2D dilaton-gravity, deformations of the minimal string, and matrix models
Turiaci, G. J., Usatyuk, M., & Weng, W. W. (2021) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ac25df · Cited by 73 · see citing works
Perturbative Finiteness in Spin-Foam Quantum Gravity
Crane, L., Perez, A., & Rovelli, C. (2001) · Physical Review Letters · doi:10.1103/physrevlett.87.181301 · Cited by 64 · see citing works
Eichhorn, A., & Koslowski, T. (2014) · Physical Review D · doi:10.1103/physrevd.90.104039 · Cited by 51 · see citing works
Matrix ensembles with global symmetries and ’t Hooft anomalies from 2d gauge theory
Kapec, D., Mahajan, R., & Stanford, D. (2020) · Journal of High Energy Physics · doi:10.1007/jhep04(2020)186 · Cited by 45 · see citing works
2D dilaton gravity in a unitary gauge
Miković, A. (1993) · Physics Letters B · doi:10.1016/0370-2693(93)91402-9 · Cited by 38 · see citing works
- Authors
- Douglas, M. R., & Shenker, S. H.
- Affiliations
- Rutgers, The State University of New Jersey (US)
- Venue
- Nuclear Physics B
- Publisher
- Elsevier BV
- Published
- 1990-05
- Volume
- 335
- Issue
- 3
- Pages
- 635-654
- ISSN
- 0550-3213 (ISSN-L)
- OpenAlex
- W1987143739
- Cited by
- 1,103
- References
- 1
- Citations by year
- 2026: 10 · 2025: 22 · 2024: 25 · 2023: 22 · 2022: 18 · 2021: 25 · 2020: 23 · 2019: 18 · 2018: 13 · 2017: 16 · 2016: 33 · 2015: 19 · 2014: 18 · 2013: 19 · 2012: 20
- FWCI
- 125.30
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Nuclear Physics B (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- 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
- Keywords
- random triangulations, two-dimensional quantum gravity, continuum limit, partition function, string perturbation theory, universality class, multicritical point, non-perturbative string theory, nonlinear ordinary differential equations, Painlevé transcendents
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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.
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