# 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:

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)

### 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 00:29:00. See the history of this page for a list of all contributions to it.