Abstract
The infrared behavior of gravity in 4D asymptotically flat spacetime exhibits a rich set of symmetries. This has led to a proposed holographic duality between the gravitational \( \mathcal{S} \)-matrix and a dual field theory living on the celestial sphere. Most of our current understanding of the dictionary relies on knowledge of the 4D bulk. As such, identifying intrinsic 2D models that capture the correct symmetries and soft dynamics of 4D gravity is an active area of interest. Here we propose that a 2D generalization of SYK provides an instructive toy model for the soft limit of the gravitational sector in 4D asymptotically flat spacetime. We find that the symmetries and soft dynamics of the 2D SYK model capture the salient features of the celestial theory: exhibiting chaotic dynamics, conformal invariance, and a w1+∞ symmetry. The holographic map from 2D SYK operators to the 4D bulk employs the Penrose twistor transform.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory, arXiv:1703.05448 [INSPIRE].
A.-M. Raclariu, Lectures on Celestial Holography, arXiv:2107.02075 [INSPIRE].
S. Pasterski, Lectures on celestial amplitudes, Eur. Phys. J. C 81 (2021) 1062 [arXiv:2108.04801] [INSPIRE].
A. Strominger, On BMS Invariance of Gravitational Scattering, JHEP 07 (2014) 152 [arXiv:1312.2229] [INSPIRE].
S. Pasterski, S.-H. Shao and A. Strominger, Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere, Phys. Rev. D 96 (2017) 065026 [arXiv:1701.00049] [INSPIRE].
S. Pasterski and S.-H. Shao, Conformal basis for flat space amplitudes, Phys. Rev. D 96 (2017) 065022 [arXiv:1705.01027] [INSPIRE].
S. Pasterski, S.-H. Shao and A. Strominger, Gluon Amplitudes as 2d Conformal Correlators, Phys. Rev. D 96 (2017) 085006 [arXiv:1706.03917] [INSPIRE].
C. Cheung, A. de la Fuente and R. Sundrum, 4D scattering amplitudes and asymptotic symmetries from 2D CFT, JHEP 01 (2017) 112 [arXiv:1609.00732] [INSPIRE].
L. Donnay, A. Puhm and A. Strominger, Conformally Soft Photons and Gravitons, JHEP 01 (2019) 184 [arXiv:1810.05219] [INSPIRE].
N. Arkani-Hamed, M. Pate, A.-M. Raclariu and A. Strominger, Celestial amplitudes from UV to IR, JHEP 08 (2021) 062 [arXiv:2012.04208] [INSPIRE].
S. Pasterski, A. Puhm and E. Trevisani, Revisiting the conformally soft sector with celestial diamonds, JHEP 11 (2021) 143 [arXiv:2105.09792] [INSPIRE].
A. Puhm, Conformally Soft Theorem in Gravity, JHEP 09 (2020) 130 [arXiv:1905.09799] [INSPIRE].
T. Adamo, L. Mason and A. Sharma, Celestial amplitudes and conformal soft theorems, Class. Quant. Grav. 36 (2019) 205018 [arXiv:1905.09224] [INSPIRE].
A. Guevara, Notes on Conformal Soft Theorems and Recursion Relations in Gravity, arXiv:1906.07810 [INSPIRE].
K. Nguyen and J. Salzer, The effective action of superrotation modes, JHEP 02 (2021) 108 [arXiv:2008.03321] [INSPIRE].
S. Pasterski and H. Verlinde, Chaos in celestial CFT, JHEP 08 (2022) 106 [arXiv:2201.01630] [INSPIRE].
A. Guevara, E. Himwich, M. Pate and A. Strominger, Holographic symmetry algebras for gauge theory and gravity, JHEP 11 (2021) 152 [arXiv:2103.03961] [INSPIRE].
A. Strominger, w(1+infinity) and the Celestial Sphere, arXiv:2105.14346 [INSPIRE].
E. Himwich, M. Pate and K. Singh, Celestial operator product expansions and w1+∞ symmetry for all spins, JHEP 01 (2022) 080 [arXiv:2108.07763] [INSPIRE].
T. Adamo, L. Mason and A. Sharma, Celestial w1+∞ Symmetries from Twistor Space, SIGMA 18 (2022) 016 [arXiv:2110.06066] [INSPIRE].
A. Ball, S. A. Narayanan, J. Salzer and A. Strominger, Perturbatively exact w1+∞ asymptotic symmetry of quantum self-dual gravity, JHEP 01 (2022) 114 [arXiv:2111.10392] [INSPIRE].
J. Mago, L. Ren, A. Y. Srikant and A. Volovich, Deformed w1+∞ Algebras in the Celestial CFT, arXiv:2111.11356 [INSPIRE].
L. Freidel, D. Pranzetti and A.-M. Raclariu, Higher spin dynamics in gravity and w1+∞ celestial symmetries, arXiv:2112.15573 [INSPIRE].
K. Costello and N. M. Paquette, Celestial holography meets twisted holography: 4d amplitudes from chiral correlators, arXiv:2201.02595 [INSPIRE].
G. Turiaci and H. Verlinde, Towards a 2d QFT Analog of the SYK Model, JHEP 10 (2017) 167 [arXiv:1701.00528] [INSPIRE].
A. Kitaev, A simple model of quantum holography, KITP Seminar (2015), http://online.kitp.ucsb.edu/online/entangled15/kitaev.
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].
S. Sachdev, Bekenstein-Hawking Entropy and Strange Metals, Phys. Rev. X 5 (2015) 041025 [arXiv:1506.05111] [INSPIRE].
J. Polchinski and V. Rosenhaus, The Spectrum in the Sachdev-Ye-Kitaev Model, JHEP 04 (2016) 001 [arXiv:1601.06768] [INSPIRE].
J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].
S. Stieberger and T. R. Taylor, Symmetries of Celestial Amplitudes, Phys. Lett. B 793 (2019) 141 [arXiv:1812.01080] [INSPIRE].
L. Donnay, S. Pasterski and A. Puhm, Asymptotic Symmetries and Celestial CFT, JHEP 09 (2020) 176 [arXiv:2005.08990] [INSPIRE].
M. Pate, A.-M. Raclariu and A. Strominger, Conformally Soft Theorem in Gauge Theory, Phys. Rev. D 100 (2019) 085017 [arXiv:1904.10831] [INSPIRE].
S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140 (1965) B516 [INSPIRE].
T. He, V. Lysov, P. Mitra and A. Strominger, BMS supertranslations and Weinberg’s soft graviton theorem, JHEP 05 (2015) 151 [arXiv:1401.7026] [INSPIRE].
F. Cachazo and A. Strominger, Evidence for a New Soft Graviton Theorem, arXiv:1404.4091 [INSPIRE].
D. Kapec, V. Lysov, S. Pasterski and A. Strominger, Semiclassical Virasoro symmetry of the quantum gravity S -matrix, JHEP 08 (2014) 058 [arXiv:1406.3312] [INSPIRE].
C. P. Boyer and J. F. Plebanski, An infinite hierarchy of conservation laws and nonlinear superposition principles for selfdual Einstein spaces, J. Math. Phys. 26 (1985) 229 [INSPIRE].
Q.-H. Park, Extended Conformal Symmetries in Real Heavens, Phys. Lett. B 236 (1990) 429 [INSPIRE].
Q.-H. Park, Selfdual Gravity as a Large N Limit of the Two-dimensional Nonlinear σ Model, Phys. Lett. B 238 (1990) 287 [INSPIRE].
L. Mason, H-space: a universal integrable system?, Twistor Newsletter 30 (1990) 14.
R. Penrose, Nonlinear Gravitons and Curved Twistor Theory, Gen. Rel. Grav. 7 (1976) 31 [INSPIRE].
S. Pasterski and A. Puhm, Shifting spin on the celestial sphere, Phys. Rev. D 104 (2021) 086020 [arXiv:2012.15694] [INSPIRE].
T. Adamo, L. Mason and A. Sharma, Twistor sigma models for quaternionic geometry and graviton scattering, arXiv:2103.16984 [INSPIRE].
K. Jensen, Chaos in AdS2 Holography, Phys. Rev. Lett. 117 (2016) 111601 [arXiv:1605.06098] [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].
B. Lian, S. L. Sondhi and Z. Yang, The chiral SYK model, JHEP 09 (2019) 067 [arXiv:1906.03308] [INSPIRE].
J. S. Cotler et al., Black Holes and Random Matrices, JHEP 05 (2017) 118 [Erratum ibid. 09 (2018) 002] [arXiv:1611.04650] [INSPIRE].
D. Stanford, Aspects of the SYK Model, 2d Gravity, and Random Matrices, Israel Institute for Advanced Studies (2019), https://www.youtube.com/watch?v=GfF8EjiLM4I.
M. Berkooz, M. Isachenkov, V. Narovlansky and G. Torrents, Towards a full solution of the large N double-scaled SYK model, JHEP 03 (2019) 079 [arXiv:1811.02584] [INSPIRE].
A. Hodges, A simple formula for gravitational MHV amplitudes, arXiv:1204.1930 [INSPIRE].
A. Alekseev and S. L. Shatashvili, Path Integral Quantization of the Coadjoint Orbits of the Virasoro Group and 2D Gravity, Nucl. Phys. B 323 (1989) 719 [INSPIRE].
J. Cotler and K. Jensen, A theory of reparameterizations for AdS3 gravity, JHEP 02 (2019) 079 [arXiv:1808.03263] [INSPIRE].
T. G. Mertens, G. J. Turiaci and H. L. Verlinde, Solving the Schwarzian via the Conformal Bootstrap, JHEP 08 (2017) 136 [arXiv:1705.08408] [INSPIRE].
E. Witten, Perturbative gauge theory as a string theory in twistor space, Commun. Math. Phys. 252 (2004) 189 [hep-th/0312171] [INSPIRE].
N. Arkani-Hamed, F. Cachazo, C. Cheung and J. Kaplan, The S-matrix in Twistor Space, JHEP 03 (2010) 110 [arXiv:0903.2110] [INSPIRE].
A. Sharma, Ambidextrous light transforms for celestial amplitudes, JHEP 01 (2022) 031 [arXiv:2107.06250] [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: 2201.05054
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
Pasterski, S., Verlinde, H. Mapping SYK to the sky. J. High Energ. Phys. 2022, 47 (2022). https://doi.org/10.1007/JHEP09(2022)047
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2022)047