Abstract
We study the end of the world (EOW) brane in double scaled SYK (DSSYK) model. We find that the boundary state of EOW brane is a coherent state of the q-deformed oscillators and the associated orthogonal polynomial is the continuous big q-Hermite polynomial. In a certain scaling limit, the big q-Hermite polynomial reduces to the Whittaker function, which reproduces the wavefunction of JT gravity with an EOW brane. We also compute the half-wormhole amplitude in DSSYK and show that the amplitude is decomposed into the trumpet and the factor coming from the EOW brane.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.S. Cotler et al., Black Holes and Random Matrices, JHEP 05 (2017) 118 [Erratum ibid. 09 (2018) 002] [arXiv:1611.04650] [INSPIRE].
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].
H.W. Lin, The bulk Hilbert space of double scaled SYK, JHEP 11 (2022) 060 [arXiv:2208.07032] [INSPIRE].
D.L. Jafferis, D.K. Kolchmeyer, B. Mukhametzhanov and J. Sonner, JT gravity with matter, generalized ETH, and Random Matrices, arXiv:2209.02131 [INSPIRE].
G. Penington, S.H. Shenker, D. Stanford and Z. Yang, Replica wormholes and the black hole interior, JHEP 03 (2022) 205 [arXiv:1911.11977] [INSPIRE].
P. Gao, D.L. Jafferis and D.K. Kolchmeyer, An effective matrix model for dynamical end of the world branes in Jackiw-Teitelboim gravity, JHEP 01 (2022) 038 [arXiv:2104.01184] [INSPIRE].
A. Goel, V. Narovlansky and H. Verlinde, Semiclassical geometry in double-scaled SYK, arXiv:2301.05732 [INSPIRE].
B. Mukhametzhanov, Large p SYK from chord diagrams, arXiv:2303.03474 [INSPIRE].
K. Okuyama and K. Suzuki, Correlators of double scaled SYK at one-loop, JHEP 05 (2023) 117 [arXiv:2303.07552] [INSPIRE].
D. Stanford and E. Witten, Fermionic Localization of the Schwarzian Theory, JHEP 10 (2017) 008 [arXiv:1703.04612] [INSPIRE].
I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products, Academic Press (2014), [INSPIRE].
S.J. Suh, Dynamics of black holes in Jackiw-Teitelboim gravity, JHEP 03 (2020) 093 [arXiv:1912.00861] [INSPIRE].
Z. Yang, The Quantum Gravity Dynamics of Near Extremal Black Holes, JHEP 05 (2019) 205 [arXiv:1809.08647] [INSPIRE].
A. Kitaev and S.J. Suh, Statistical mechanics of a two-dimensional black hole, JHEP 05 (2019) 198 [arXiv:1808.07032] [INSPIRE].
D.K. Kolchmeyer, von Neumann algebras in JT gravity, JHEP 06 (2023) 067 [arXiv:2303.04701] [INSPIRE].
E.J. Martinec, The annular report on noncritical string theory, hep-th/0305148 [INSPIRE].
P. Saad, S.H. Shenker and D. Stanford, JT gravity as a matrix integral, arXiv:1903.11115 [INSPIRE].
K. Okuyama, Hartle-Hawking wavefunction in double scaled SYK, JHEP 03 (2023) 152 [arXiv:2212.09213] [INSPIRE].
M. Berkooz, V. Narovlansky and H. Raj, Complex Sachdev-Ye-Kitaev model in the double scaling limit, JHEP 02 (2021) 113 [arXiv:2006.13983] [INSPIRE].
M. Berkooz, N. Brukner, V. Narovlansky and A. Raz, Multi-trace correlators in the SYK model and non-geometric wormholes, JHEP 21 (2020) 196 [arXiv:2104.03336] [INSPIRE].
G. Akemann and P.H. Damgaard, Wilson loops in N = 4 supersymmetric Yang-Mills theory from random matrix theory, Phys. Lett. B 513 (2001) 179 [hep-th/0101225] [INSPIRE].
S. Giombi, V. Pestun and R. Ricci, Notes on supersymmetric Wilson loops on a two-sphere, JHEP 07 (2010) 088 [arXiv:0905.0665] [INSPIRE].
K. Okuyama, Connected correlator of 1/2 BPS Wilson loops in \( \mathcal{N} \) = 4 SYM, JHEP 10 (2018) 037 [arXiv:1808.10161] [INSPIRE].
J. Ambjorn, J. Jurkiewicz and Y.M. Makeenko, Multiloop correlators for two-dimensional quantum gravity, Phys. Lett. B 251 (1990) 517 [INSPIRE].
E. Brezin and A. Zee, Universality of the correlations between eigenvalues of large random matrices, Nucl. Phys. B 402 (1993) 613 [INSPIRE].
K. Okuyama and K. Sakai, FZZT branes in JT gravity and topological gravity, JHEP 09 (2021) 191 [arXiv:2108.03876] [INSPIRE].
M. Berkooz, M. Isachenkov, P. Narayan and V. Narovlansky, Quantum groups, non-commutative AdS2, and chords in the double-scaled SYK model, arXiv:2212.13668 [INSPIRE].
T. Sasamoto, One-dimensional partially asymmetric simple exclusion process with open boundaries: orthogonal polynomials approach, J. Phys. A 32 (1999) 7109.
N. Crampe, E. Ragoucy and M. Vanicat, Integrable approach to simple exclusion processes with boundaries. Review and progress, J. Stat. Mech. 1411 (2014) P11032 [arXiv:1408.5357] [INSPIRE].
R. Floreanini, J. LeTourneux and L. Vinet, An algebraic interpretation of the continuous big q-hermite polynomials, J. Math. Phys. 36 (1995) 5091 [math/9504217].
M.E.H. Ismail and D. Stanton, On the Askey-Wilson and Rogers Polynomials, Can. J. Math. 40 (1988) 1025.
Acknowledgments
The author would like to thank Satoru Odake and Kenta Suzuki for discussion. This work was supported in part by JSPS Grant-in-Aid for Transformative Research Areas (A) “Extreme Universe” 21H05187 and JSPS KAKENHI Grant 22K03594.
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: 2305.12674
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
Okuyama, K. End of the world brane in double scaled SYK. J. High Energ. Phys. 2023, 53 (2023). https://doi.org/10.1007/JHEP08(2023)053
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2023)053