# nLab Jackiw-Teitelboim gravity

Contents

### Context

#### Gravity

gravity, supergravity

# Contents

## Idea

JT-gravity (Teitelboim 83, Jackiw 85) is gravity in 1+1 dimensions with a dilaton.

## Properties

### Relation to near-extremal black holes

JT-gravity gives a good approximation to the AdS-factor in the near horizon geometry $AdS_2\times S^{d-2}$ of near-extremal black holes in $d$-dimensional spacetime (NSST18, MTV18).

Via the AdS/CFT-dual of JT-gravity (Almheiri-Polchinski 14) given by random matrix theory (Saad-Shenker-Stanford 19, Stanford-Witten 19) (or SYK model) this allows to compute genuine quantum gravity-aspects of near-extremal black holes, such as notable their microscopic black hole entropy. Computations are now under way…

Notice that near-extremal black holes have been observed in nature, by the Chandra telescope see eg here.

## References

### General

The theory is due to

Further development:

• Andreas Blommaert, Thomas G. Mertens, Henri Verschelde, Eigenbranes in Jackiw-Teitelboim gravity (arXiv:1911.11603)

Via twistors:

• Wolfgang Wieland, Twistor representation of Jackiw-Teitelboim gravity (arXiv:2003.13887)

### SYK-model in $AdS_2/CFT_1$

Discussion of the SYK-model as the AdS/CFT dual of JT-gravity in nearly AdS2/CFT1 and AdS-CFT in condensed matter physics:

Original articles:

Review:

Relation to black holes in terms of Majorana dimer states:

• Ioanna Kourkoulou, Juan Maldacena, Pure states in the SYK model and nearly-$AdS_2$ gravity (arXiv:1707.02325)

Relation to black holes in string theory and random matrix theory:

• Yuri D. Lensky, Xiao-Liang Qi, Pengfei Zhang, Size of bulk fermions in the SYK model (arXiv:2002.01961)

• Xiao-Liang Qi, Pengfei Zhang, The Coupled SYK model at Finite Temperature (arXiv:2003.03916)

• Akash Goel, Herman Verlinde, Towards a String Dual of SYK (arXiv:2103.03187)

• Tarek Anous, Felix M. Haehl, The quantum $p$-spin glass model: A user manual for holographers (arXiv:2106.03838)

Discussion of small N corrections via a lattice QFT-Ansatz on the AdS side:

• Richard C. Brower, Cameron V. Cogburn, A. Liam Fitzpatrick, Dean Howarth, Chung-I Tan, Lattice Setup for Quantum Field Theory in $AdS_2$ (arXiv:1912.07606)

• Gregory J. Galloway, Melanie Graf, Eric Ling, A conformal infinity approach to asymptotically $AdS_2 \times S^{n-1}$ spacetimes (arXiv:2003.00093)

### BFSS matrix model in $AdS_2/CFT_1$

On AdS2/CFT1 with the BFSS matrix model on the CFT side and black hole-like solutions in type IIA supergravity on the AdS side:

and on its analog of holographic entanglement entropy:

• Takeshi Morita, Hiroki Yoshida, A Critical Dimension in One-dimensional Large-N Reduced Models (arXiv:2001.02109)

### Chord diagrams and weight systems in Physics

The following is a list of references that involve (weight systems on) chord diagrams/Jacobi diagrams in physics:

For a unifying perspective (via Hypothesis H) and further pointers, see:

Review:

#### In Chern-Simons theory

Since weight systems are the associated graded of Vassiliev invariants, and since Vassiliev invariants are knot invariants arising as certain correlators/Feynman amplitudes of Chern-Simons theory in the presence of Wilson lines, there is a close relation between weight systems and quantum Chern-Simons theory.

Historically this is the original application of chord diagrams/Jacobi diagrams and their weight systems, see also at graph complex and Kontsevich integral.

Reviewed in:

Applied to Gopakumar-Vafa duality:

• Dave Auckly, Sergiy Koshkin, Introduction to the Gopakumar-Vafa Large $N$ Duality, Geom. Topol. Monogr. 8 (2006) 195-456 (arXiv:0701568)

#### For single trace operators in AdS/CFT duality

Interpretation of Lie algebra weight systems on chord diagrams as certain single trace operators, in particular in application to black hole thermodynamics

#### In $AdS_2/CFT_1$, JT-gravity/SYK-model

Discussion of (Lie algebra-)weight systems on chord diagrams as SYK model single trace operators:

• Antonio M. García-García, Yiyang Jia, Jacobus J. M. Verbaarschot, Exact moments of the Sachdev-Ye-Kitaev model up to order $1/N^2$, JHEP 04 (2018) 146 (arXiv:1801.02696)

• Yiyang Jia, Jacobus J. M. Verbaarschot, Section 4 of: Large $N$ expansion of the moments and free energy of Sachdev-Ye-Kitaev model, and the enumeration of intersection graphs, JHEP 11 (2018) 031 (arXiv:1806.03271)

• Micha Berkooz, Prithvi Narayan, Joan Simón, Chord diagrams, exact correlators in spin glasses and black hole bulk reconstruction, JHEP 08 (2018) 192 (arxiv:1806.04380)

following:

• László Erdős, Dominik Schröder, Phase Transition in the Density of States of Quantum Spin Glasses, D. Math Phys Anal Geom (2014) 17: 9164 (arXiv:1407.1552)

which in turn follows

• Philippe Flajolet, Marc Noy, Analytic Combinatorics of Chord Diagrams, pages 191–201 in Daniel Krob, Alexander A. Mikhalev,and Alexander V. Mikhalev, (eds.), Formal Power Series and Algebraic Combinatorics, Springer 2000 (doi:10.1007/978-3-662-04166-6_17)

With emphasis on the holographic content:

• Micha Berkooz, Mikhail Isachenkov, Vladimir Narovlansky, Genis Torrents, Section 5 of: Towards a full solution of the large $N$ double-scaled SYK model, JHEP 03 (2019) 079 (arxiv:1811.02584)

• Vladimir Narovlansky, Slide 23 (of 28) of: Towards a Solution of Large $N$ Double-Scaled SYK, 2019 (pdf)

• Micha Berkooz, Mikhail Isachenkov, Prithvi Narayan, Vladimir Narovlansky, Quantum groups, non-commutative $AdS_2$, and chords in the double-scaled SYK model &lbrack;arXiv:2212.13668&rbrack;

and specifically in relation, under AdS2/CFT1, to Jackiw-Teitelboim gravity:

#### As codes for holographic entanglement entropy

Chord diagrams encoding Majorana dimer codes and other quantum error correcting codes via tensor networks exhibiting holographic entanglement entropy:

#### For Dyson-Schwinger equations

Discussion of round chord diagrams organizing Dyson-Schwinger equations:

• Nicolas Marie, Karen Yeats, A chord diagram expansion coming from some Dyson-Schwinger equations, Communications in Number Theory and Physics, 7(2):251291, 2013 (arXiv:1210.5457)

• Markus Hihn, Karen Yeats, Generalized chord diagram expansions of Dyson-Schwinger equations, Ann. Inst. Henri Poincar Comb. Phys. Interact. 6 no 4:573-605 (arXiv:1602.02550)

Review in:

• Ali Assem Mahmoud, Section 3 of: On the Enumerative Structures in Quantum Field Theory (arXiv:2008.11661)

### Application to near-extremal near-horizons

Application to near horizon geometry of near-extremal black holes:

### Lift to string/M-theory

Realization of JT-gravity as Kaluza-Klein reduction of D=6 supergravity on the worldvolume of D1-D5 brane bound states or M2-M5 brane bound states:

• Yue-Zhou Li, Shou-Long Li, H. Lu, Exact Embeddings of JT Gravity in Strings and M-theory, Eur. Phys. J. C (2018) 78: 791 (arXiv:1804.09742)

• Iosif Bena, Pierre Heidmann, David Turton, $AdS_2$ Holography: Mind the Cap, JHEP 1812 (2018) 028 (arXiv:1806.02834)

• Giuseppe Dibitetto, Nicolò Petri, $AdS_2$ solutions and their massive IIA origin, JHEP 05 (2019) 107 (arXiv:1811.11572)

• Junho Hong, Niall Macpherson, Leopoldo A. Pando Zayas, Aspects of $AdS_2$ classification in M-theory: Solutions with mesonic and baryonic charges, JHEP 11 (2019) 127 (arXiv:1908.08518)

### In terms of weight systems on chord diagrams

Discussion of (Lie algebra-)weight systems on chord diagrams encoding JT gravity observables

(for more see at weight systems on chord diagrams in physics):

and similarly, under AdS2/CFT1, as correlators in the SYK model:

• Antonio M. García-García, Yiyang Jia, Jacobus J. M. Verbaarschot, Exact moments of the Sachdev-Ye-Kitaev model up to order $1/N^2$, JHEP 04 (2018) 146 (arXiv:1801.02696)

• Micha Berkooz, Prithvi Narayan, Joan Simón, Chord diagrams, exact correlators in spin glasses and black hole bulk reconstruction, JHEP 08 (2018) 192 (arxiv:1806.04380)

following:

• László Erdős, Dominik Schröder, Phase Transition in the Density of States of Quantum Spin Glasses, D. Math Phys Anal Geom (2014) 17: 9164 (arXiv:1407.1552)

which in turn follows

• Philippe Flajolet, Marc Noy, Analytic Combinatorics of Chord Diagrams, pages 191–201 in Daniel Krob, Alexander A. Mikhalev,and Alexander V. Mikhalev, (eds.), Formal Power Series and Algebraic Combinatorics, Springer 2000 (doi:10.1007/978-3-662-04166-6_17)

With emphasis on holographic content:

• Micha Berkooz, Mikhail Isachenkov, Vladimir Narovlansky, Genis Torrents, Section 5 of: Towards a full solution of the large $N$ double-scaled SYK model, JHEP 03 (2019) 079 (arxiv:1811.02584)

• Vladimir Narovlansky, Slide 23 (of 28) of: Towards a Solution of Large $N$ Double-Scaled SYK, 2019 (pdf)

Last revised on January 11, 2021 at 05:29:00. See the history of this page for a list of all contributions to it.