Abstract
We construct the non-relativistic and Carrollian versions of Jackiw-Teitelboim gravity. In the second order formulation, there are no divergences in the non-relativistic and Carrollian limits. Instead, in the first order formalism, some divergences can be avoided by starting from a relativistic BF theory with (A)dS2 × ℝ gauge algebra. We show how to define the boundary duals of the gravity actions using the method of non-linear realisations and suitable Inverse Higgs constraints. In particular, the non-relativistic version of the Schwarzian action is constructed in this way. We derive the asymptotic symmetries of the theory, as well as the corresponding conserved charges and Newton-Cartan geometric structure. Finally, we show how the same construction applies to the Carrollian case.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Sachdev and J. Ye, Gapless spin fluid ground state in a random, quantum Heisenberg magnet, Phys. Rev. Lett. 70 (1993) 3339 [cond-mat/9212030] [INSPIRE].
A. Kitaev, A simple model of quantum holography (part 1), talk at KITP, April 7, 2015, http://online.kitp.ucsb.edu/online/entangled15/kitaev/.
A. Kitaev, A simple model of quantum holography (part 2), talk at KITP, May 27, 2015, http://online.kitp.ucsb.edu/online/entangled15/kitaev2/.
A. Kitaev and S.J. Suh, The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual, JHEP 05 (2018) 183 [arXiv:1711.08467] [INSPIRE].
C. Teitelboim, Gravitation and Hamiltonian Structure in Two Space-Time Dimensions, Phys. Lett. B 126 (1983) 41 [INSPIRE].
R. Jackiw, Lower Dimensional Gravity, Nucl. Phys. B 252 (1985) 343 [INSPIRE].
J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].
D. Stanford and E. Witten, Fermionic Localization of the Schwarzian Theory, JHEP 10 (2017) 008 [arXiv:1703.04612] [INSPIRE].
J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space, PTEP 2016 (2016) 12C104 [arXiv:1606.01857] [INSPIRE].
J. Engelsöy, T.G. Mertens and H. Verlinde, An investigation of AdS2 backreaction and holography, JHEP 07 (2016) 139 [arXiv:1606.03438] [INSPIRE].
K. Jensen, Chaos in AdS2 Holography, Phys. Rev. Lett. 117 (2016) 111601 [arXiv:1605.06098] [INSPIRE].
S. Sachdev, Bekenstein-Hawking Entropy and Strange Metals, Phys. Rev. X 5 (2015) 041025 [arXiv:1506.05111] [INSPIRE].
R.A. Davison, W. Fu, A. Georges, Y. Gu, K. Jensen and S. Sachdev, Thermoelectric transport in disordered metals without quasiparticles: The Sachdev-Ye-Kitaev models and holography, Phys. Rev. B 95 (2017) 155131 [arXiv:1612.00849] [INSPIRE].
K. Bulycheva, A note on the SYK model with complex fermions, JHEP 12 (2017) 069 [arXiv:1706.07411] [INSPIRE].
P. Chaturvedi, Y. Gu, W. Song and B. Yu, A note on the complex SYK model and warped CFTs, JHEP 12 (2018) 101 [arXiv:1808.08062] [INSPIRE].
Y. Gu, A. Kitaev, S. Sachdev and G. Tarnopolsky, Notes on the complex Sachdev-Ye-Kitaev model, JHEP 02 (2020) 157 [arXiv:1910.14099] [INSPIRE].
V. Godet and C. Marteau, New boundary conditions for AdS2, JHEP 12 (2020) 020 [arXiv:2005.08999] [INSPIRE].
H. Afshar, H.A. González, D. Grumiller and D. Vassilevich, Flat space holography and the complex Sachdev-Ye-Kitaev model, Phys. Rev. D 101 (2020) 086024 [arXiv:1911.05739] [INSPIRE].
A.R. Brown, H. Gharibyan, H.W. Lin, L. Susskind, L. Thorlacius and Y. Zhao, Complexity of Jackiw-Teitelboim gravity, Phys. Rev. D 99 (2019) 046016 [arXiv:1810.08741] [INSPIRE].
L. Susskind, Complexity and Newton’s Laws, Front. in Phys. 8 (2020) 262 [arXiv:1904.12819] [INSPIRE].
J.L.F. Barbón, J. Martin-Garcia and M. Sasieta, Proof of a Momentum/Complexity Correspondence, Phys. Rev. D 102 (2020) 101901 [arXiv:2006.06607] [INSPIRE].
D.E. Berenstein, J.M. Maldacena and H.S. Nastase, Strings in flat space and pp waves from N = 4 superYang-Mills, JHEP 04 (2002) 013 [hep-th/0202021] [INSPIRE].
J. Gomis, J. Gomis and K. Kamimura, Non-relativistic superstrings: A New soluble sector of AdS5 × S5, JHEP 12 (2005) 024 [hep-th/0507036] [INSPIRE].
T. Fukuyama and K. Kamimura, Gauge Theory of Two-dimensional Gravity, Phys. Lett. B 160 (1985) 259 [INSPIRE].
K. Isler and C.A. Trugenberger, A Gauge Theory of Two-dimensional Quantum Gravity, Phys. Rev. Lett. 63 (1989) 834 [INSPIRE].
A.H. Chamseddine and D. Wyler, Gauge Theory of Topological Gravity in (1+1)-Dimensions, Phys. Lett. B 228 (1989) 75 [INSPIRE].
A. Galajinsky, Schwarzian mechanics via nonlinear realizations, Phys. Lett. B 795 (2019) 277 [arXiv:1905.01935] [INSPIRE].
S.R. Coleman, J. Wess and B. Zumino, Structure of phenomenological Lagrangians. 1, Phys. Rev. 177 (1969) 2239 [INSPIRE].
C.G. Callan Jr., S.R. Coleman, J. Wess and B. Zumino, Structure of phenomenological Lagrangians. 2, Phys. Rev. 177 (1969) 2247 [INSPIRE].
E.A. Ivanov and V.I. Ogievetsky, The Inverse Higgs Phenomenon in Nonlinear Realizations, Teor. Mat. Fiz. 25 (1975) 164 [INSPIRE].
H. Bacry and J. Levy-Leblond, Possible kinematics, J. Math. Phys. 9 (1968) 1605 [INSPIRE].
J. Derome and J.G. Dubouis, Hooke’s symmetries and nonrelativistic cosmological model kinematics, Nuovo Cim. B 9 (1972) 351.
J.M. Lévy-Leblond, Une nouvelle limite non-relativiste du group de Poincaré, Ann. Inst. H. Poincaré 3 (1965) 1.
M. Ba nados, Global charges in Chern-Simons field theory and the (2+1) black hole, Phys. Rev. D 52 (1996) 5816 [hep-th/9405171] [INSPIRE].
E. Cartan, Sur les variétés à connexion affine et la théorie de la relativité généralisée. (première partie), Annales Sci. Ecole Norm. Sup. 40 (1923) 325.
E. Cartan, Sur les variétés à connexion affine et la théorie de la relativité généralisée. (première partie) (Suite), Annales Sci. Ecole Norm. Sup. 41 (1924) 1.
A. Trautman, Sur la Théorie Newtonienne de la Gravitation, Compt. Rend. Acad. Sci. 257 (1963) 617.
P. HAVAS, Four-Dimensional Formulations of Newtonian Mechanics and Their Relation to the Special and the General Theory of Relativity, Rev. Mod. Phys. 36 (1964) 938 [INSPIRE].
H.P. Kuenzle, Galilei and lorentz structures on space-time — comparison of the corresponding geometry and physics, Ann. Inst. H. Poincare Phys. Theor. 17 (1972) 337 [INSPIRE].
K. Kuchar, Gravitation, geometry, and nonrelativistic quantum theory, Phys. Rev. D 22 (1980) 1285 [INSPIRE].
M. Henneaux, Geometry of Zero Signature Space-times, Bull. Soc. Math. Belg. 31 (1979) 47 [INSPIRE].
C. Duval, G.W. Gibbons, P.A. Horvathy and P.M. Zhang, Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time, Class. Quant. Grav. 31 (2014) 085016 [arXiv:1402.0657] [INSPIRE].
D. Hansen, J. Hartong and N.A. Obers, Non-Relativistic Gravity and its Coupling to Matter, JHEP 06 (2020) 145 [arXiv:2001.10277] [INSPIRE].
R. De Pietri, L. Lusanna and M. Pauri, Standard and generalized Newtonian gravities as ‘gauge’ theories of the extended Galilei group. I. The standard theory, Class. Quant. Grav. 12 (1995) 219 [gr-qc/9405046] [INSPIRE].
D. Van den Bleeken, Torsional Newton-Cartan gravity from the large c expansion of general relativity, Class. Quant. Grav. 34 (2017) 185004 [arXiv:1703.03459] [INSPIRE].
E. Bergshoeff, J.M. Izquierdo, T. Ortín and L. Romano, Lie Algebra Expansions and Actions for Non-Relativistic Gravity, JHEP 08 (2019) 048 [arXiv:1904.08304] [INSPIRE].
D. Grumiller, J. Hartong, S. Prohazka and J. Salzer, Limits of JT gravity, JHEP 02 (2021) 134 [arXiv:2011.13870] [INSPIRE].
A. Barducci, R. Casalbuoni and J. Gomis, Confined dynamical systems with Carroll and Galilei symmetries, Phys. Rev. D 98 (2018) 085018 [arXiv:1804.10495] [INSPIRE].
E. Bergshoeff, J.M. Izquierdo and L. Romano, Carroll versus Galilei from a Brane Perspective, JHEP 10 (2020) 066 [arXiv:2003.03062] [INSPIRE].
R. Jackiw, Gauge theories for lineal gravities, in International Conference on Interface Between Physics and Mathematics, (1993) [hep-th/9309082] [INSPIRE].
S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, John Wiley and Sons, New York U.S.A. (1972).
G. Dautcourt, Die newtonske gravitationstheorie als strenger grenzfall der allgemeinen relativitätheorie, Acta Phys. Pol 25 (1964) 637.
J. Ehlers, Republication of: On the Newtonian limit of Einstein’s theory of gravitation, Gen. Rel. Grav. 51 (2019) 163 [INSPIRE].
G. Dautcourt, On the ultrarelativistic limit of general relativity, Acta Phys. Polon. B 29 (1998) 1047 [gr-qc/9801093] [INSPIRE].
E. Bergshoeff, J. Rosseel and T. Zojer, Newton-Cartan (super)gravity as a non-relativistic limit, Class. Quant. Grav. 32 (2015) 205003 [arXiv:1505.02095] [INSPIRE].
R. Andringa, E. Bergshoeff, S. Panda and M. de Roo, Newtonian Gravity and the Bargmann Algebra, Class. Quant. Grav. 28 (2011) 105011 [arXiv:1011.1145] [INSPIRE].
T. Regge and C. Teitelboim, Role of Surface Integrals in the Hamiltonian Formulation of General Relativity, Annals Phys. 88 (1974) 286 [INSPIRE].
E. Frodden and D. Hidalgo, Surface Charges Toolkit for Gravity, Int. J. Mod. Phys. D 29 (2020) 2050040 [arXiv:1911.07264] [INSPIRE].
D. Grumiller, M. Leston and D. Vassilevich, Anti-de Sitter holography for gravity and higher spin theories in two dimensions, Phys. Rev. D 89 (2014) 044001 [arXiv:1311.7413] [INSPIRE].
W. Siegel, Conformal Invariance of Extended Spinning Particle Mechanics, Int. J. Mod. Phys. A 3 (1988) 2713 [INSPIRE].
J. Gomis, J. Herrero, K. Kamimura and J. Roca, Diffeomorphisms, nonlinear W symmetries and particle models, Annals Phys. 244 (1995) 67 [hep-th/9309048] [INSPIRE].
A.M. Polyakov, Gauge Transformations and Diffeomorphisms, Int. J. Mod. Phys. A 5 (1990) 833 [INSPIRE].
V.G. Drinfeld and V.V. Sokolov, Lie algebras and equations of Korteweg-de Vries type, J. Sov. Math. 30 (1984) 1975 [INSPIRE].
P. Saad, S.H. Shenker and D. Stanford, JT gravity as a matrix integral, arXiv:1903.11115 [INSPIRE].
D.M. Hofman and B. Rollier, Warped Conformal Field Theory as Lower Spin Gravity, Nucl. Phys. B 897 (2015) 1 [arXiv:1411.0672] [INSPIRE].
O. Coussaert, M. Henneaux and P. van Driel, The Asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant, Class. Quant. Grav. 12 (1995) 2961 [gr-qc/9506019] [INSPIRE].
D. Hansen, J. Hartong and N.A. Obers, Action Principle for Newtonian Gravity, Phys. Rev. Lett. 122 (2019) 061106 [arXiv:1807.04765] [INSPIRE].
N. Ozdemir, M. Ozkan, O. Tunca and U. Zorba, Three-Dimensional Extended Newtonian (Super)Gravity, JHEP 05 (2019) 130 [arXiv:1903.09377] [INSPIRE].
J. Gomis, A. Kleinschmidt, J. Palmkvist and P. Salgado-ReboLledó, Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity, JHEP 02 (2020) 009 [arXiv:1912.07564] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2011.15053
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Gomis, J., Hidalgo, D. & Salgado-Rebolledo, P. Non-relativistic and Carrollian limits of Jackiw-Teitelboim gravity. J. High Energ. Phys. 2021, 162 (2021). https://doi.org/10.1007/JHEP05(2021)162
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2021)162