De Sitter Space has no Chords. Almost Everything is Confined.

Document Type : Regular article


Stanford Institute for Theoretical Physics and Department of Physics


This paper describes a phenomenon in which all but a tiny fraction of the fundamental holographic degrees of the SYK theory are confined (as in quark confinement) in the double-scaled infinite temperature limit. The mechanism for confinement is an essential ingredient in the duality between DSSYK and de Sitter space.

The mechanism, which removes almost all states from the physical spectrum of the bulk de Sitter theory applies to configurations of a small number of fermions which would be expected to comprise Hawking radiation in de Sitter space. Without confinement there would be far too many species of Hawking particles. The mechanism also applies to configurations with larger number of fermions, including the objects described by chord diagrams.


Main Subjects


Article PDF

[1] L. Susskind, “De Sitter Space, Double-Scaled SYK, and the Separation of Scales in the Semiclassical Limit,” [arXiv:2209.09999 [hep-th]]
[2] A. A. Rahman, “dS JT Gravity and Double-Scaled SYK,” [arXiv:2209.09997 [hep-th]].
[3] M. Berkooz, M. Isachenkov, V. Narovlansky and G. Torrents, “Towards a full solution of the large N double-scaled SYK model,” JHEP 03, 079 (2019) doi:10.1007/JHEP03(2019)079 [arXiv:1811.02584 [hep-th]].
[4] H. W. Lin, “The bulk Hilbert space of double scaled SYK,” JHEP 11, 060 (2022) doi:10.1007/JHEP11(2022)060 [arXiv:2208.07032 [hep-th]].
[5] J. Maldacena and D. Stanford, “Remarks on the Sachdev-Ye-Kitaev model,” Phys. Rev. D 94, no.10, 106002 (2016) doi:10.1103/PhysRevD.94.106002 [arXiv:1604.07818 [hep-th]].
[6] J. S. Cotler, G. Gur-Ari, M. Hanada, J. Polchinski, P. Saad, S. H. Shenker, D. Stanford, A. Streicher and M. Tezuka, “Black Holes and Random Matrices,” JHEP 05, 118 (2017) [erratum: JHEP 09, 002 (2018)] doi:10.1007/JHEP05(2017)118 [arXiv:1611.04650 [hep-th]].
[7] X. Dong, E. Silverstein and G. Torroba, “De Sitter Holography and Entanglement Entropy,” JHEP 07, 050 (2018) doi:10.1007/JHEP07(2018)050 [arXiv:1804.08623 [hep-th]].
[8] V. Chandrasekaran, R. Longo, G. Penington and E. Witten, “An algebra of observables for de Sitter space,” JHEP 02, 082 (2023) doi:10.1007/JHEP02(2023)082 [arXiv:2206.10780 [hep-th]].
[9] H. Lin and L. Susskind, “Infinite Temperature’s Not So Hot,” [arXiv:2206.01083 [hep-th]].
[10] M. Berkooz, V. Narovlansky and H. Raj, “Complex Sachdev-Ye-Kitaev model in the double scaling limit,” JHEP 02, 113 (2021) doi:10.1007/JHEP02(2021)113 [arXiv:2006.13983 [hep-th]].
[11] L. Susskind, “Electric Forces in the Charged SYK Model,” [arXiv:2012.12326 [hep-th]].
[12] L. Susskind, “Scrambling in Double-Scaled SYK and De Sitter Space,” [arXiv:2205.00315 [hep-th]].
[13] D. A. Roberts, D. Stanford and A. Streicher, “Operator growth in the SYK model,” JHEP 06, 122 (2018) doi:10.1007/JHEP06(2018)122 [arXiv:1802.02633 [hep-th]].
[14] J. Polchinski, L. Susskind and N. Toumbas, “Negative energy, superluminosity and holography,” Phys. Rev. D 60, 084006 (1999) doi:10.1103/PhysRevD.60.084006 [arXiv:hep-th/9903228 [hep-th]].
[15] T. Banks, B. Fiol and A. Morisse, “Towards a quantum theory of de Sitter space,” JHEP 12, 004 (2006) doi:10.1088/1126-6708/2006/12/004 [arXiv:hep-th/0609062 [hep-th]].
[16] L. Susskind, “Black Holes Hint Towards De Sitter-Matrix Theory,” [arXiv:2109.01322 [hep-th]].
[17] L. Susskind, “Entanglement and Chaos in De Sitter Space Holography: An SYK Ex- ample,” JHAP 1 (1) 1-22 (2021) doi:10.22128/jhap.2021.455.1005 [arXiv:2109.14104 [hep-th]].
Volume 3, Issue 1
March 2023
Pages 1-30
  • Receive Date: 01 March 2023
  • Revise Date: 21 March 2023
  • Accept Date: 31 March 2023