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P. Saad, S. Shenker, and D. Stanford, “JT Gravity As A Matrix Integral,” arXiv:1903.11115
Original
1903
Earlier work this paper cites.
T. G. Mertens and G. Turiaci, “Defects in Jackiw-Teitelboim Quantum Gravity,” arXiv:1904.05228
Original
1904
Earlier work this paper cites.
J. Cotler, K. Jensen, and A. Maloney, “Low-dimensional de Sitter Quantum Gravity,” arXiv:1905.03780
Original
1905
Earlier work this paper cites.
D. Stanford and E. Witten, “JT Gravity And The Ensembles Of Random Matrix Theory,” arXiv:1907.03363
Original
1907
Earlier work this paper cites.
M. F. Atiyah, “Resolution of Singularities and Division of Distributions,” Comm. Pure Appl. Math. 23
1970
Earlier work this paper cites.
E. Brézin, C. Itzykson, G. Parisi, and J.-B. Zuber, “Planar Diagrams,” Comm. Math. Phys. 59
1978
Earlier work this paper cites.
D. Weingarten, “Euclidean Quantum Gravity On A Lattice,” Nucl. Phys. B210
1982
Earlier work this paper cites.
C. Teitelboim, “Gravitation and Hamiltonian Structure in Two Space-Time Dimensions,” Phys. Lett. B126
1983
Earlier work this paper cites.
R. Jackiw, “Lower Dimensional Gravity,” Nucl. Phys. B252
1985
Earlier work this paper cites.
V. Kazakov, “Bilocal Regularization Of Models Of Random Surfaces,” Phys. Lett. 150B
1985
Earlier work this paper cites.

Similar

F. David, “Randomly Triangulated Surfaces In Two Dimensions,” Nucl. Phys. B257
1985
Cited alongside, same era.
J. Ambjorn, B. Durhuus, and J. Frohlich, “Diseases of Triangulated Random Surfaces, and Possible Cures,” Nucl. Phys. B257
1985
Cited alongside, same era.
V. Kazakov, I. Kostov, and A. Migdal, “Critical Properties Of Randomly Triangulated Planar Random Surfaces,” Phys. Lett. 157B
1985
Cited alongside, same era.
D. Kutasov, “Geometry on the Space of Conformal Field Theories and Contact Terms,” Phys. Lett. B220
1989
Cited alongside, same era.
E. Brézin and V. Kazakov, “Exactly Solvable Field Theories Of Closed Strings,” Phys. Lett. B236
1990
Cited alongside, same era.
M. Douglas and S. Shenker, “Strings In Less Than One Dimension,” Nucl. Phys. B335

Then

N. Ikeda, “Two-Dimensional Gravity and Nonlinear Gauge Theory,” Ann. Phys. 235
1994
Later among the works it cites.
P. Di Francesco, P. H. Ginsparg, and J. Zinn-Justin, “2-D Gravity and Random Matrices,” Phys. Rept. 254
1995
Later among the works it cites.
E. Witten, “Deformations of JT Gravity And Phase Transitions,” arXiv:2006.03494
Original
2006
Later among the works it cites.
H. Maxfield and G. Turiaci, “The Path Integral of 3D Gravity Near Extremality, or JT Gravity WIth Defects as a Matrix Integral,” arXiv:2006.11317
Original
2006
Later among the works it cites.
T. G. Mertens and G. Turiaci, “Liouville Quantum Gravity – Holography, JT, and Matrices,” arXiv:2006.07072
Original
2006
Later among the works it cites.

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2020

Matrix Models and Deformations of JT Gravity

Witten, Edward

Understand

Recently, it has been found that JT gravity, which is a two-dimensional theory with bulk action $ -\frac{1}{2}\int {\mathrm d}^2x \sqrt g\phi(R+2)$, is dual to a matrix model, that is, a random ensemble of quantum systems rather than a specific quantum mechanical system.

In this article, we argue that a deformation of JT gravity with bulk action $ -\frac{1}{2}\int {\mathrm d}^2x \sqrt g(\phi R+W(\phi))$ is likewise dual to a matrix model.
With a specific procedure for defining the path integral of the theory, we determine the density of eigenvalues of the dual matrix model.
There is a simple answer if $W(0)=0$, and otherwise a rather complicated answer.

Built on

P. Saad, S. Shenker, and D. Stanford, “JT Gravity As A Matrix Integral,” arXiv:1903.11115
Original
1903
Earlier work this paper cites.
T. G. Mertens and G. Turiaci, “Defects in Jackiw-Teitelboim Quantum Gravity,” arXiv:1904.05228
Original
1904
Earlier work this paper cites.
J. Cotler, K. Jensen, and A. Maloney, “Low-dimensional de Sitter Quantum Gravity,” arXiv:1905.03780
Original
1905
Earlier work this paper cites.
D. Stanford and E. Witten, “JT Gravity And The Ensembles Of Random Matrix Theory,” arXiv:1907.03363
Original
1907
Earlier work this paper cites.
M. F. Atiyah, “Resolution of Singularities and Division of Distributions,” Comm. Pure Appl. Math. 23
1970
Earlier work this paper cites.
E. Brézin, C. Itzykson, G. Parisi, and J.-B. Zuber, “Planar Diagrams,” Comm. Math. Phys. 59
1978
Earlier work this paper cites.
D. Weingarten, “Euclidean Quantum Gravity On A Lattice,” Nucl. Phys. B210
1982
Earlier work this paper cites.
C. Teitelboim, “Gravitation and Hamiltonian Structure in Two Space-Time Dimensions,” Phys. Lett. B126
1983
Earlier work this paper cites.
R. Jackiw, “Lower Dimensional Gravity,” Nucl. Phys. B252
1985
Earlier work this paper cites.
V. Kazakov, “Bilocal Regularization Of Models Of Random Surfaces,” Phys. Lett. 150B
1985
Earlier work this paper cites.

Similar

F. David, “Randomly Triangulated Surfaces In Two Dimensions,” Nucl. Phys. B257
1985
Cited alongside, same era.
J. Ambjorn, B. Durhuus, and J. Frohlich, “Diseases of Triangulated Random Surfaces, and Possible Cures,” Nucl. Phys. B257
1985
Cited alongside, same era.
V. Kazakov, I. Kostov, and A. Migdal, “Critical Properties Of Randomly Triangulated Planar Random Surfaces,” Phys. Lett. 157B
1985
Cited alongside, same era.
D. Kutasov, “Geometry on the Space of Conformal Field Theories and Contact Terms,” Phys. Lett. B220
1989
Cited alongside, same era.
E. Brézin and V. Kazakov, “Exactly Solvable Field Theories Of Closed Strings,” Phys. Lett. B236
1990
Cited alongside, same era.
M. Douglas and S. Shenker, “Strings In Less Than One Dimension,” Nucl. Phys. B335

Then

N. Ikeda, “Two-Dimensional Gravity and Nonlinear Gauge Theory,” Ann. Phys. 235
1994
Later among the works it cites.
P. Di Francesco, P. H. Ginsparg, and J. Zinn-Justin, “2-D Gravity and Random Matrices,” Phys. Rept. 254
1995
Later among the works it cites.
E. Witten, “Deformations of JT Gravity And Phase Transitions,” arXiv:2006.03494
Original
2006
Later among the works it cites.
H. Maxfield and G. Turiaci, “The Path Integral of 3D Gravity Near Extremality, or JT Gravity WIth Defects as a Matrix Integral,” arXiv:2006.11317
Original
2006
Later among the works it cites.
T. G. Mertens and G. Turiaci, “Liouville Quantum Gravity – Holography, JT, and Matrices,” arXiv:2006.07072
Original
2006
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

1990

Cited alongside, same era.

D. J. Gross and A. Migdal, “Nonperturbative Two-Dimensional Quantum Gravity,” Phys. Rev. Lett. 64

1990

Cited alongside, same era.

T. Banks and M. O’Loughlin, “Two-Dimensional Quantum Gravity In Minkowski Space,” Nucl. Phys. B362

1991

Cited alongside, same era.

E. Witten, “Two-Dimensional Gravity And Intersection Theory On Moduli Space,” Surveys Diff. Geom. 1

1991

Cited alongside, same era.

D. Louis-Martinez, J. Gegenberg, and G. Kunstatter, “Exact Quantization of All 2 − D 2-D Dilaton Gravity Theories,” Phys. Lett. B321

1994

Cited alongside, same era.

P. Ginsparg and G. Moore, “Lectures on 2D Gravity And 2D String Theory,” hep-th/9304011

Cited in the paper.

B. Eynard and N. Orantin, “Weil-Petersson Volume of Moduli Spaces, Mirzakhani’s Recursion and Matrix Models,” arXiv:0705.3600

Original

Cited in the paper.

S. P. Tan, Y. L. Wong, and Y. Zhang, “Generalizations Of McShane’s Identity To Hyperbolic Cone-Surfaces,” J. Diff. Geom. 72

2006

Later among the works it cites.

M. Mirzakhani, “Weil-Petersson Volumes and Intersection Theory On The Moduli Space Of Curves,” Journal AMS 20

2007

Later among the works it cites.

D. Stanford and E. Witten, “Fermionic Localization Of The Schwarzian Theory,” JHEP 10

Original

2017

Later among the works it cites.

R. Dijkgraaf and E. Witten, “Developments in Topological Gravity,” Int. J. Mod. Phys. A33

Original

2018

Later among the works it cites.