Abstract
We demonstrate the turbulent dynamics of the Nambu-Goto open string in the AdS3 spacetime. While the motion of a classical closed string in AdS is known to be integrable, the integrability of an open string motion depends on the boundary conditions at the string endpoints. We numerically solve the equations of motion of the open string under the boundary conditions where the endpoints are i) fixed to a finite radial coordinate in AdS, and ii) free. For i), we find turbulence on the string, that shows a cascade in the energy and angular momentum spectra. This result indicates the non-integrability of the open string with this type of boundary conditions. For ii), we find no turbulence. This is consistent with the integrability of the open string with the free boundary conditions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].
N. Beisert et al., Review of AdS/CFT Integrability: An Overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].
G. Mandal, N.V. Suryanarayana and S.R. Wadia, Aspects of semiclassical strings in AdS5, Phys. Lett. B 543 (2002) 81 [hep-th/0206103] [INSPIRE].
I. Bena, J. Polchinski and R. Roiban, Hidden Symmetries of the AdS5 × S5 Superstring, Phys. Rev. D 69 (2004) 046002 [hep-th/0305116] [INSPIRE].
K. Yoshida, Yang-Baxter Deformation of 2D Non-Linear Sigma Models. Towards applications to AdS/CFT, Springer Nature (2020) [https://doi.org/10.1007/978-981-16-1703-4].
J.M. Evans, M. Hassan, N.J. MacKay and A.J. Mountain, Local conserved charges in principal chiral models, Nucl. Phys. B 561 (1999) 385 [hep-th/9902008] [INSPIRE].
N.J. MacKay and B.J. Short, Boundary scattering, symmetric spaces and the principal chiral model on the half line, Commun. Math. Phys. 233 (2003) 313 [hep-th/0104212] [INSPIRE].
G.W. Delius, N.J. MacKay and B.J. Short, Boundary remnant of Yangian symmetry and the structure of rational reflection matrices, Phys. Lett. B 522 (2001) 335 [hep-th/0109115] [INSPIRE].
N. Mann and S.E. Vazquez, Classical Open String Integrability, JHEP 04 (2007) 065 [hep-th/0612038] [INSPIRE].
A. Dekel and Y. Oz, Integrability of Green-Schwarz Sigma Models with Boundaries, JHEP 08 (2011) 004 [arXiv:1106.3446] [INSPIRE].
N. MacKay and V. Regelskis, Achiral boundaries and the twisted Yangian of the D5-brane, JHEP 08 (2011) 019 [arXiv:1105.4128] [INSPIRE].
S.-J. Rey and J.-T. Yee, Macroscopic strings as heavy quarks in large N gauge theory and anti-de Sitter supergravity, Eur. Phys. J. C 22 (2001) 379 [hep-th/9803001] [INSPIRE].
J.M. Maldacena, Wilson loops in large N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [INSPIRE].
T. Ishii, K. Murata and K. Yoshida, Boundary driven turbulence on string worldsheet, JHEP 01 (2024) 073 [arXiv:2310.08124] [INSPIRE].
P. Basu and L.A. Pando Zayas, Analytic Non-integrability in String Theory, Phys. Rev. D 84 (2011) 046006 [arXiv:1105.2540] [INSPIRE].
K.S. Rigatos, Non-integrability in AdS3 vacua, JHEP 02 (2021) 032 [arXiv:2011.08224] [INSPIRE].
L.A. Pando Zayas and C.A. Terrero-Escalante, Chaos in the Gauge / Gravity Correspondence, JHEP 09 (2010) 094 [arXiv:1007.0277] [INSPIRE].
P. Basu, D. Das and A. Ghosh, Integrability Lost, Phys. Lett. B 699 (2011) 388 [arXiv:1103.4101] [INSPIRE].
P. Basu and L.A. Pando Zayas, Chaos rules out integrability of strings on AdS5 × T1,1, Phys. Lett. B 700 (2011) 243 [arXiv:1103.4107] [INSPIRE].
Y. Asano, D. Kawai, H. Kyono and K. Yoshida, Chaotic strings in a near Penrose limit of AdS5 × T1,1, JHEP 08 (2015) 060 [arXiv:1505.07583] [INSPIRE].
T. Ishii, K. Murata and K. Yoshida, Fate of chaotic strings in a confining geometry, Phys. Rev. D 95 (2017) 066019 [arXiv:1610.05833] [INSPIRE].
S. Kushiro and K. Yoshida, Chaotic string motion in a near pp-wave limit, JHEP 01 (2023) 065 [arXiv:2209.05171] [INSPIRE].
K.L. Panigrahi and M. Samal, Chaos in classical string dynamics in \( \hat{\gamma} \) deformed AdS5 × T1,1, Phys. Lett. B 761 (2016) 475 [arXiv:1605.05638] [INSPIRE].
T. Ishii, S. Kushiro and K. Yoshida, Chaotic string dynamics in deformed T1,1, JHEP 05 (2021) 158 [arXiv:2103.12416] [INSPIRE].
K. Hashimoto, K. Murata and N. Tanahashi, Chaos of Wilson Loop from String Motion near Black Hole Horizon, Phys. Rev. D 98 (2018) 086007 [arXiv:1803.06756] [INSPIRE].
T. Akutagawa, K. Hashimoto, K. Murata and T. Ota, Chaos of QCD string from holography, Phys. Rev. D 100 (2019) 046009 [arXiv:1903.04718] [INSPIRE].
T. Ishii and K. Murata, Turbulent strings in AdS/CFT, JHEP 06 (2015) 086 [arXiv:1504.02190] [INSPIRE].
T. Ishii and K. Murata, Dynamical AdS strings across horizons, JHEP 03 (2016) 035 [arXiv:1512.08574] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, A semiclassical limit of the gauge / string correspondence, Nucl. Phys. B 636 (2002) 99 [hep-th/0204051] [INSPIRE].
P. Bizoń and A. Rostworowski, On weakly turbulent instability of anti-de Sitter space, Phys. Rev. Lett. 107 (2011) 031102 [arXiv:1104.3702] [INSPIRE].
P. Bizoń and J. Jałmużna, Globally regular instability of AdS3, Phys. Rev. Lett. 111 (2013) 041102 [arXiv:1306.0317] [INSPIRE].
E. Ott, Chaos in Dynamical Systems, second edition, Cambridge University Press (2002) [https://doi.org/10.1017/CBO9780511803260].
Acknowledgments
The authors would like to thank Dimitrios Giataganas and Kentaroh Yoshida for valuable discussions. The work of T.I. was supported in part by JSPS KAKENHI Grant Number 19K03871. The work of R.K. was financially supported by JST SPRING, Grant Number JPMJSP2125. R.K. would like to take this opportunity to thank “Interdisciplinary Frontier Next-Generation Researcher Program of the Tokai Higher Education and Research System.” The work of K.M. was supported in part by JSPS KAKENHI Grant Nos. 20K03976, 21H05186 and 22H01217. The work of C.Y. was supported in part by JSPS KAKENHI Grant Nos. 20H05850 and 20H05853.
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: 2310.19317
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
Ishii, T., Kitaku, R., Murata, K. et al. Turbulence on open string worldsheets under non-integrable boundary conditions. J. High Energ. Phys. 2024, 149 (2024). https://doi.org/10.1007/JHEP02(2024)149
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2024)149