Abstract
Holography has provided valuable insights into the time evolution of strongly coupled gauge theories in a fixed spacetime. However, this framework is insufficient if this spacetime is dynamical. We present a scheme to evolve a four-dimensional, strongly interacting gauge theory coupled to four-dimensional dynamical gravity in the semiclassical regime. As in previous work, we use holography to evolve the quantum gauge theory stress tensor, whereas the four-dimensional metric evolves according to Einstein’s equations coupled to the expectation value of the stress tensor. The novelty of our approach is that both the boundary and the bulk spacetimes are constructed dynamically, one time step at a time. We focus on Friedmann-Lemaître-Robertson-Walker geometries and evolve far-from-equilibrium initial states that lead to asymptotically expanding, flat or collapsing Universes.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal and U.A. Wiedemann, Gauge/String Duality, Hot QCD and Heavy Ion Collisions, Cambridge University Press (2014) [DOI] [arXiv:1101.0618] [INSPIRE].
W. Busza, K. Rajagopal and W. van der Schee, Heavy Ion Collisions: The Big Picture, and the Big Questions, Ann. Rev. Nucl. Part. Sci. 68 (2018) 339 [arXiv:1802.04801] [INSPIRE].
J. Zaanen, Y.-W. Sun, Y. Liu and K. Schalm, Holographic Duality in Condensed Matter Physics, Cambridge University Press (2015) [DOI] [INSPIRE].
S.A. Hartnoll, A. Lucas and S. Sachdev, Holographic quantum matter, arXiv:1612.07324 [INSPIRE].
H. Nastase, String Theory Methods for Condensed Matter Physics, Cambridge University Press (2017) [DOI] [INSPIRE].
D. Marolf, M. Rangamani and T. Wiseman, Holographic thermal field theory on curved spacetimes, Class. Quant. Grav. 31 (2014) 063001 [arXiv:1312.0612] [INSPIRE].
A. Buchel, Gauge/gravity correspondence in accelerating universe, Phys. Rev. D 65 (2002) 125015 [hep-th/0203041] [INSPIRE].
J. Maldacena and G.L. Pimentel, Entanglement entropy in de Sitter space, JHEP 02 (2013) 038 [arXiv:1210.7244] [INSPIRE].
W. Fischler, S. Kundu and J.F. Pedraza, Entanglement and out-of-equilibrium dynamics in holographic models of de Sitter QFTs, JHEP 07 (2014) 021 [arXiv:1311.5519] [INSPIRE].
A. Buchel, Verlinde Gravity and AdS/CFT, arXiv:1702.08590 [INSPIRE].
A. Buchel, Ringing in de Sitter spacetime, Nucl. Phys. B 928 (2018) 307 [arXiv:1707.01030] [INSPIRE].
A. Buchel, χSB of cascading gauge theory in de Sitter, JHEP 05 (2020) 035 [arXiv:1912.03566] [INSPIRE].
A. Buchel, Entanglement entropy of \( \mathcal{N} \) = 2* de Sitter vacuum, Nucl. Phys. B 948 (2019) 114769 [arXiv:1904.09968] [INSPIRE].
J. Casalderrey-Solana, C. Ecker, D. Mateos and W. Van Der Schee, Strong-coupling dynamics and entanglement in de Sitter space, JHEP 03 (2021) 181 [arXiv:2011.08194] [INSPIRE].
H. Friedrich, Einstein equations and conformal structure — Existence of anti de Sitter type space-times, J. Geom. Phys. 17 (1995) 125 [INSPIRE].
A. Enciso and N. Kamran, Lorentzian Einstein metrics with prescribed conformal infinity, J. Diff. Geom. 112 (2019) 505 [arXiv:1412.4376] [INSPIRE].
D.A. Carranza and J.A. Valiente Kroon, Construction of anti-de Sitter-like spacetimes using the metric conformal Einstein field equations: the vacuum case, Class. Quant. Grav. 35 (2018) 245006 [arXiv:1807.04212] [INSPIRE].
G.T. Horowitz and D. Wang, Gravitational Corner Conditions in Holography, JHEP 01 (2020) 155 [arXiv:1909.11703] [INSPIRE].
C. Csáki, M. Graesser, C.F. Kolda and J. Terning, Cosmology of one extra dimension with localized gravity, Phys. Lett. B 462 (1999) 34 [hep-ph/9906513] [INSPIRE].
A. Kehagias and E. Kiritsis, Mirage cosmology, JHEP 11 (1999) 022 [hep-th/9910174] [INSPIRE].
J.M. Cline, C. Grojean and G. Servant, Cosmological expansion in the presence of extra dimensions, Phys. Rev. Lett. 83 (1999) 4245 [hep-ph/9906523] [INSPIRE].
C. Csáki, M. Graesser, L. Randall and J. Terning, Cosmology of brane models with radion stabilization, Phys. Rev. D 62 (2000) 045015 [hep-ph/9911406] [INSPIRE].
S.S. Gubser, AdS/CFT and gravity, Phys. Rev. D 63 (2001) 084017 [hep-th/9912001] [INSPIRE].
G.R. Dvali, G. Gabadadze and M. Porrati, Metastable gravitons and infinite volume extra dimensions, Phys. Lett. B 484 (2000) 112 [hep-th/0002190] [INSPIRE].
A. Karch and L. Randall, Locally localized gravity, JHEP 05 (2001) 008 [hep-th/0011156] [INSPIRE].
E. Kiritsis, Holography and brane-bulk energy exchange, JCAP 10 (2005) 014 [hep-th/0504219] [INSPIRE].
P.S. Apostolopoulos, G. Siopsis and N. Tetradis, Cosmology from an AdS Schwarzschild black hole via holography, Phys. Rev. Lett. 102 (2009) 151301 [arXiv:0809.3505] [INSPIRE].
G. Compere and D. Marolf, Setting the boundary free in AdS/CFT, Class. Quant. Grav. 25 (2008) 195014 [arXiv:0805.1902] [INSPIRE].
J. Erdmenger, K. Ghoroku and R. Meyer, Holographic (De)confinement Transitions in Cosmological Backgrounds, Phys. Rev. D 84 (2011) 026004 [arXiv:1105.1776] [INSPIRE].
X. Dong, B. Horn, S. Matsuura, E. Silverstein and G. Torroba, FRW solutions and holography from uplifted AdS/CFT, Phys. Rev. D 85 (2012) 104035 [arXiv:1108.5732] [INSPIRE].
S. Banerjee, S. Bhowmick, A. Sahay and G. Siopsis, Generalized Holographic Cosmology, Class. Quant. Grav. 30 (2013) 075022 [arXiv:1207.2983] [INSPIRE].
S. Fischetti, D. Kastor and J. Traschen, Non-Vacuum AdS Cosmologies and the Approach to Equilibrium of Entanglement Entropy, Class. Quant. Grav. 31 (2014) 235007 [arXiv:1407.4299] [INSPIRE].
A. Buchel and A. Karapetyan, de Sitter Vacua of Strongly Interacting QFT, JHEP 03 (2017) 114 [arXiv:1702.01320] [INSPIRE].
P.M. Chesler and A. Loeb, Holographic duality and mode stability of de Sitter space in semiclassical gravity, JCAP 11 (2020) 010 [arXiv:2003.05501] [INSPIRE].
J.K. Ghosh, E. Kiritsis, F. Nitti and L.T. Witkowski, Back-reaction in massless de Sitter QFTs: holography, gravitational DBI action and f(R) gravity, JCAP 07 (2020) 040 [arXiv:2003.09435] [INSPIRE].
R. Emparan, A.M. Frassino and B. Way, Quantum BTZ black hole, JHEP 11 (2020) 137 [arXiv:2007.15999] [INSPIRE].
A. Buchel, M.P. Heller and J. Noronha, Entropy Production, Hydrodynamics, and Resurgence in the Primordial Quark-Gluon Plasma from Holography, Phys. Rev. D 94 (2016) 106011 [arXiv:1603.05344] [INSPIRE].
S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217 (2001) 595 [hep-th/0002230] [INSPIRE].
M. Bianchi, D.Z. Freedman and K. Skenderis, How to go with an RG flow, JHEP 08 (2001) 041 [hep-th/0105276] [INSPIRE].
M. Bianchi, D.Z. Freedman and K. Skenderis, Holographic renormalization, Nucl. Phys. B 631 (2002) 159 [hep-th/0112119] [INSPIRE].
N.D. Birrell and P.C.W. Davies, Quantum Fields in Curved Space, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, U.K. (1984) [DOI] [INSPIRE].
C. Fefferman and C.R. Graham, Conformal invariants, in Élie Cartan et les mathématiques d’aujourd’hui Lyon, 25–29 juin 1984, no. S131 in Astérisque, Société mathématique de France (1985) [http://www.numdam.org/item/AST_1985_S131_95_0/].
P.M. Chesler and L.G. Yaffe, Horizon formation and far-from-equilibrium isotropization in supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 102 (2009) 211601 [arXiv:0812.2053] [INSPIRE].
M.P. Heller, R.A. Janik and P. Witaszczyk, The characteristics of thermalization of boost-invariant plasma from holography, Phys. Rev. Lett. 108 (2012) 201602 [arXiv:1103.3452] [INSPIRE].
M.P. Heller, D. Mateos, W. van der Schee and D. Trancanelli, Strong Coupling Isotropization of Non-Abelian Plasmas Simplified, Phys. Rev. Lett. 108 (2012) 191601 [arXiv:1202.0981] [INSPIRE].
L. Kofman, A.D. Linde and A.A. Starobinsky, Reheating after inflation, Phys. Rev. Lett. 73 (1994) 3195 [hep-th/9405187] [INSPIRE].
L. Kofman, A.D. Linde and A.A. Starobinsky, Towards the theory of reheating after inflation, Phys. Rev. D 56 (1997) 3258 [hep-ph/9704452] [INSPIRE].
V.F. Mukhanov, L.R.W. Abramo and R.H. Brandenberger, On the Back reaction problem for gravitational perturbations, Phys. Rev. Lett. 78 (1997) 1624 [gr-qc/9609026] [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: 2109.10355
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
Ecker, C., van der Schee, W., Mateos, D. et al. Holographic evolution with dynamical boundary gravity. J. High Energ. Phys. 2022, 137 (2022). https://doi.org/10.1007/JHEP03(2022)137
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2022)137