Abstract
We extend the study of the non-linear perturbative theory of weakly turbulent energy cascades in AdSd+1 to include solutions of driven systems, i.e. those with time-dependent sources on the AdS boundary. This necessitates the activation of non-normalizable modes in the linear solution for the massive bulk scalar field, which couple to the metric and normalizable scalar modes. We determine analytic expressions for secular terms in the renormalization flow equations mass values \( {m}_{BF}^2<{m}^2\le 0 \), and for various driving functions. Finally, we numerically evaluate these sources for d = 4 and discuss what role these driven solutions play in the perturbative stability of AdS.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G. Martinon, The instability of Anti-de Sitter space-time, arXiv:1708.05600 [INSPIRE].
V.E. Hubeny, The AdS/CFT correspondence, Class. Quant. Grav. 32 (2015) 124010 [arXiv:1501.00007] [INSPIRE].
P. Bizon and A. Rostworowski, On weakly turbulent instability of Anti-de Sitter space, Phys. Rev. Lett. 107 (2011) 031102 [arXiv:1104.3702] [INSPIRE].
O.J.C. Dias, G.T. Horowitz, D. Marolf and J.E. Santos, On the nonlinear stability of asymptotically Anti-de Sitter solutions, Class. Quant. Grav. 29 (2012) 235019 [arXiv:1208.5772] [INSPIRE].
M.W. Choptuik, O.J.C. Dias, J.E. Santos and B. Way, Collapse and nonlinear instability of AdS space with angular momentum, Phys. Rev. Lett. 119 (2017) 191104 [arXiv:1706.06101] [INSPIRE].
L.-Y. Chen, N. Goldenfeld and Y. Oono, The renormalization group and singular perturbations: multiple scales, boundary layers and reductive perturbation theory, Phys. Rev. E 54 (1996) 376 [hep-th/9506161] [INSPIRE].
Y. Nakayama, Holographic interpretation of renormalization group approach to singular perturbations in nonlinear differential equations, Phys. Rev. D 88 (2013) 105006 [arXiv:1305.4117] [INSPIRE].
D. Garfinkle and L.A. Pando Zayas, Rapid thermalization in field theory from gravitational collapse, Phys. Rev. D 84 (2011) 066006 [arXiv:1106.2339] [INSPIRE].
J. Jalmuzna, A. Rostworowski and P. Bizon, A comment on AdS collapse of a scalar field in higher dimensions, Phys. Rev. D 84 (2011) 085021 [arXiv:1108.4539] [INSPIRE].
M. Choptuik, J.E. Santos and B. Way, Charting Islands of Stability with Multioscillators in anti–de Sitter space, Phys. Rev. Lett. 121 (2018) 021103 [arXiv:1803.02830] [INSPIRE].
B. Cownden, N. Deppe and A.R. Frey, Phase diagram of stability for massive scalars in Anti-de Sitter spacetime, Phys. Rev. D 102 (2020) 026015 [arXiv:1711.00454] [INSPIRE].
S.L. Liebling and G. Khanna, Scalar collapse in AdS with an OpenCL open source code, Class. Quant. Grav. 34 (2017) 205012 [arXiv:1706.07413] [INSPIRE].
N. Deppe and A.R. Frey, Classes of stable initial data for massless and massive scalars in Anti-de Sitter spacetime, JHEP 12 (2015) 004 [arXiv:1508.02709] [INSPIRE].
V. Balasubramanian, A. Buchel, S.R. Green, L. Lehner and S.L. Liebling, Holographic thermalization, stability of Anti-de Sitter space, and the Fermi-Pasta-Ulam paradox, Phys. Rev. Lett. 113 (2014) 071601 [arXiv:1403.6471] [INSPIRE].
R. Auzzi, S. Elitzur, S.B. Gudnason and E. Rabinovici, On periodically driven AdS/CFT, JHEP 11 (2013) 016 [arXiv:1308.2132] [INSPIRE].
B. Craps, O. Evnin, P. Jai-akson and J. Vanhoof, Ultraviolet asymptotics for quasiperiodic AdS4 perturbations, JHEP 10 (2015) 080 [arXiv:1508.05474] [INSPIRE].
B. Craps, O. Evnin and J. Vanhoof, Renormalization group, secular term resummation and AdS (in) stability, JHEP 10 (2014) 048 [arXiv:1407.6273] [INSPIRE].
B. Craps, O. Evnin and J. Vanhoof, Renormalization, averaging, conservation laws and AdS (in)stability, JHEP 01 (2015) 108 [arXiv:1412.3249] [INSPIRE].
B. Craps, O. Evnin and J. Vanhoof, Ultraviolet asymptotics and singular dynamics of AdS perturbations, JHEP 10 (2015) 079 [arXiv:1508.04943] [INSPIRE].
N. Deppe, Resonant dynamics in higher dimensional anti-de Sitter spacetime, Phys. Rev. D 100 (2019) 124028 [arXiv:1606.02712] [INSPIRE].
F.V. Dimitrakopoulos, B. Freivogel and J.F. Pedraza, Fast and slow coherent cascades in Anti-de Sitter spacetime, Class. Quant. Grav. 35 (2018) 125008 [arXiv:1612.04758] [INSPIRE].
O. Evnin and P. Jai-akson, Detailed ultraviolet asymptotics for AdS scalar field perturbations, JHEP 04 (2016) 054 [arXiv:1602.05859] [INSPIRE].
S.R. Green, A. Maillard, L. Lehner and S.L. Liebling, Islands of stability and recurrence times in AdS, Phys. Rev. D 92 (2015) 084001 [arXiv:1507.08261] [INSPIRE].
F.V. Dimitrakopoulos, B. Freivogel, J.F. Pedraza and I.-S. Yang, Gauge dependence of the AdS instability problem, Phys. Rev. D 94 (2016) 124008 [arXiv:1607.08094] [INSPIRE].
A. Buchel, R.C. Myers and A. van Niekerk, Nonlocal probes of thermalization in holographic quenches with spectral methods, JHEP 02 (2015) 017 [Erratum ibid. 07 (2015) 137] [arXiv:1410.6201] [INSPIRE].
A. Biasi, P. Carracedo, J. Mas, D. Musso and A. Serantes, Floquet scalar dynamics in global AdS, JHEP 04 (2018) 137 [arXiv:1712.07637] [INSPIRE].
P. Carracedo, J. Mas, D. Musso and A. Serantes, Adiabatic pumping solutions in global AdS, JHEP 05 (2017) 141 [arXiv:1612.07701] [INSPIRE].
M. Rangamani, M. Rozali and A. Wong, Driven holographic CFTs, JHEP 04 (2015) 093 [arXiv:1502.05726] [INSPIRE].
R.C. Myers, M. Rozali and B. Way, Holographic quenches in a confined phase, J. Phys. A 50 (2017) 494002 [arXiv:1706.02438] [INSPIRE].
V. Balasubramanian, P. Kraus and A.E. Lawrence, Bulk versus boundary dynamics in Anti-de Sitter space-time, Phys. Rev. D 59 (1999) 046003 [hep-th/9805171] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Positive energy in Anti-de Sitter backgrounds and gauged extended supergravity, Phys. Lett. B 115 (1982) 197 [INSPIRE].
H. Năstase, Introduction to the ADS/CFT correspondence, Cambridge University Press, Cambridge U.K. (2015).
X. Wen and J.-Q. Wu, Floquet conformal field theory, arXiv:1805.00031 [INSPIRE].
V. Balasubramanian, P. Kraus, A.E. Lawrence and S.P. Trivedi, Holographic probes of Anti-de Sitter space-times, Phys. Rev. D 59 (1999) 104021 [hep-th/9808017] [INSPIRE].
D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Correlation functions in the CFT(d)/AdS(d+1) correspondence, Nucl. Phys. B 546 (1999) 96 [hep-th/9804058] [INSPIRE].
M. Bianchi, D.Z. Freedman and K. Skenderis, Holographic renormalization, Nucl. Phys. B 631 (2002) 159 [hep-th/0112119] [INSPIRE].
R. Manvelyan, K. Mkrtchyan and R. Mkrtchyan, Conformal invariant powers of the Laplacian, Fefferman-Graham ambient metric and Ricci gauging, Phys. Lett. B 657 (2007) 112 [arXiv:0707.1737] [INSPIRE].
E. Alvarez, J. Conde and L. Hernandez, The Dirichlet obstruction in AdS /CFT, Int. J. Mod. Phys. D 12 (2003) 1415 [hep-th/0303164] [INSPIRE].
E. Alvarez, J. Conde and L. Hernandez, Rudiments of holography, Int. J. Mod. Phys. D 12 (2003) 543 [hep-th/0205075] [INSPIRE].
C. Fefferman and C.R. Graham, The ambient metric, Ann. Math. Stud. 178 (2011) 1 [arXiv:0710.0919] [INSPIRE].
D. Martelli and W. Mueck, Holographic renormalization and Ward identities with the Hamilton-Jacobi method, Nucl. Phys. B 654 (2003) 248 [hep-th/0205061] [INSPIRE].
A. Buchel, L. Lehner and R.C. Myers, Thermal quenches in N = 2* plasmas, JHEP 08 (2012) 049 [arXiv:1206.6785] [INSPIRE].
A. Biasi, B. Craps and O. Evnin, Energy returns in global AdS4, Phys. Rev. D 100 (2019) 024008 [arXiv:1810.04753] [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: 1912.07143
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
Cownden, B. Examining instabilities due to driven scalars in AdS. J. High Energ. Phys. 2020, 13 (2020). https://doi.org/10.1007/JHEP12(2020)013
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2020)013