nLab
Jackiw-Teitelboim gravity

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.

Related concepts

• SYK model

• Liouville theory

References

General

The theory is due to

• Claudio Teitelboim, Gravitation and hamiltonian structure in two spacetime dimensions, Physics Letters B Volume 126, Issues 1–2, 23 June 1983, Pages 41-45 (doi:10.1016/0370-2693(83)90012-6

• Roman Jackiw, Lower dimensional gravity, Nuclear Physics B

  Volume 252, 1985, Pages 343-356 (doi:10.1016/0550-3213(85)90448-1)

See also

• Wikipedia, Jackiw-Teitelboim gravity

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:

• Juan Maldacena, Douglas Stanford, Comments on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94, 106002 (2016)(arXiv:1604.07818)

• Subir Sachdev, Holographic metals and the fractionalized Fermi liquid, Phys. Rev. Lett. 105:151602, 2010 (arXiv:1006.3794)

Review:

• Gábor Sárosi, $AdS_2$ holography and the SYK model, Proceedings of Science 323 (arXiv:1711.08482, doi:10.22323/1.323.0001)

• Juan Maldacena, Toy models for black holes II, talk at PiTP 2018 From QBits to spacetime (recording)

• Dmitrii A. Trunin, Pedagogical introduction to SYK model and 2D Dilaton Gravity (arXiv:2002.12187)

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:

• Jordan S. Cotler, Guy Gur-Ari, Masanori Hanada, Joseph Polchinski, Phil Saad, Stephen Shenker, Douglas Stanford, Alexandre Streicher, Masaki Tezuka, Black Holes and Random Matrices, JHEP 1705:118, 2017 (arXiv:1611.04650)

• Tomoki Nosaka, Tokiro Numasawa, Quantum Chaos, Thermodynamics and Black Hole Microstates in the mass deformed SYK model (arXiv:1912.12302)

See also

• 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)

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)

See also:

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

Random matrix theory in $AdS_2/CFT_1$

On Jackiw-Teitelboim gravity dual to random matrix theory (via AdS2/CFT1 and topological recursion):

• Ahmed Almheiri, Joseph Polchinski, Models of $AdS_2$ Backreaction and Holography, J. High Energ. Phys. (2015) 2015: 14. (arXiv:1402.6334)

• CGHSS 16

• Phil Saad, Stephen Shenker, Douglas Stanford, JT gravity as a matrix integral (arXiv:1903.11115)

• Douglas Stanford, Edward Witten, JT Gravity and the Ensembles of Random Matrix Theory (arXiv:1907.03363)

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:

• Juan Maldacena, Alexey Milekhin, To gauge or not to gauge?, JHEP 04 (2018) 084 (arxiv:1802.00428)

and on its analog of holographic entanglement entropy:

• Tarek Anous, Joanna L. Karczmarek, Eric Mintun, Mark Van Raamsdonk, Benson Way, Areas and entropies in BFSS/gravity duality (arXiv:1911.11145)

See also

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

D1-D3 brane intersections in $AdS_2/CFT_1$

On D1-D3 brane intersections in AdS2/CFT1:

• Giuseppe Dibitetto, Yolanda Lozano, Nicolò Petri, Anayeli Ramirez, Holographic Description of M-branes via $AdS_2$ (arXiv:1912.09932)

Via T-duality from D6-D8 brane intersections:

• Yolanda Lozano, Carlos Nunez, Anayeli Ramirez, Stefano Speziali, New $AdS_2$ backgrounds and $\mathcal{N}=4$ Conformal Quantum Mechanics (arXiv:2011.00005)

Application to near-extremal near-horizons

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

• Pranjal Nayak, Ashish Shukla, Ronak M Soni, Sandip Trivedi, V. Vishal, On the Dynamics of Near-Extremal Black Holes (arXiv:1802.09547)

• Upamanyu Moitra, Sandip Trivedi, V. Vishal, Near-Extremal Near-Horizons (arXiv:1808.08239)

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):

• Andreas Blommaert, Thomas Mertens, Henri Verschelde, The Schwarzian Theory - A Wilson Line Perspective, JHEP 1812 (2018) 022 (arXiv:1806.07765)

• Andreas Blommaert, Thomas Mertens, Henri Verschelde, Fine Structure of Jackiw-Teitelboim Quantum Gravity, JHEP 1909 (2019) 066 (arXiv:1812.00918)

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)