Abstract
Using numerical holography, we study the collision, at non-zero impact parameter, of bounded, localized distributions of energy density chosen to mimic relativistic heavy ion collisions, in strongly coupled \( \mathcal{N}=4 \) supersymmetric Yang-Mills theory. Both longitudinal and transverse dynamics in the dual field theory are properly described. Using the gravitational description, we solve 5D Einstein equations with no dimensionality reducing symmetry restrictions to find the asymptotically anti-de Sitter spacetime geometry. Implications of our results on the understanding of early stages of heavy ion collisions, including the development of transverse radial flow, are discussed.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E.V. Shuryak, What RHIC experiments and theory tell us about properties of quark-gluon plasma?, Nucl. Phys. A 750 (2005) 64 [hep-ph/0405066] [INSPIRE].
P.M. Chesler and L.G. Yaffe, Boost invariant flow, black hole formation and far-from-equilibrium dynamics in N = 4 supersymmetric Yang-Mills theory, Phys. Rev. D 82 (2010) 026006 [arXiv:0906.4426] [INSPIRE].
P.M. Chesler and L.G. Yaffe, Holography and colliding gravitational shock waves in asymptotically AdS 5 spacetime, Phys. Rev. Lett. 106 (2011) 021601 [arXiv:1011.3562] [INSPIRE].
J. Casalderrey-Solana, M.P. Heller, D. Mateos and W. van der Schee, From full stopping to transparency in a holographic model of heavy ion collisions, Phys. Rev. Lett. 111 (2013) 181601 [arXiv:1305.4919] [INSPIRE].
W. van der Schee, P. Romatschke and S. Pratt, Fully dynamical simulation of central nuclear collisions, Phys. Rev. Lett. 111 (2013) 222302 [arXiv:1307.2539] [INSPIRE].
H. Bantilan, F. Pretorius and S.S. Gubser, Simulation of asymptotically AdS 5 spacetimes with a generalized harmonic evolution scheme, Phys. Rev. D 85 (2012) 084038 [arXiv:1201.2132] [INSPIRE].
H. Bantilan and P. Romatschke, Simulation of black hole collisions in asymptotically Anti-de Sitter spacetimes, Phys. Rev. Lett. 114 (2015) 081601 [arXiv:1410.4799] [INSPIRE].
S.S. Gubser, S.S. Pufu and A. Yarom, Entropy production in collisions of gravitational shock waves and of heavy ions, Phys. Rev. D 78 (2008) 066014 [arXiv:0805.1551] [INSPIRE].
D. Grumiller and P. Romatschke, On the collision of two shock waves in AdS 5, JHEP 08 (2008) 027 [arXiv:0803.3226] [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].
P.M. Chesler and L.G. Yaffe, Numerical solution of gravitational dynamics in asymptotically Anti-de Sitter spacetimes, JHEP 07 (2014) 086 [arXiv:1309.1439] [INSPIRE].
S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear fluid dynamics from gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [INSPIRE].
R. Baier, P. Romatschke, D.T. Son, A.O. Starinets and M.A. Stephanov, Relativistic viscous hydrodynamics, conformal invariance and holography, JHEP 04 (2008) 100 [arXiv:0712.2451] [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].
M.P. Heller, D. Mateos, W. van der Schee and M. Triana, Holographic isotropization linearized, JHEP 09 (2013) 026 [arXiv:1304.5172] [INSPIRE].
J. Vredevoogd and S. Pratt, Universal flow in the first stage of relativistic heavy ion collisions, Phys. Rev. C 79 (2009) 044915 [arXiv:0810.4325] [INSPIRE].
M. Luzum and H. Petersen, Initial state fluctuations and final state correlations in relativistic heavy-ion collisions, J. Phys. G 41 (2014) 063102 [arXiv:1312.5503] [INSPIRE].
S. Floerchinger and U.A. Wiedemann, Statistics of initial density perturbations in heavy ion collisions and their fluid dynamic response, JHEP 08 (2014) 005 [arXiv:1405.4393] [INSPIRE].
B. Schenke, P. Tribedy and R. Venugopalan, Initial-state geometry and fluctuations in Au+Au, Cu+Au and U+U collisions at energies available at the BNL relativistic heavy ion collider, Phys. Rev. C 89 (2014) 064908 [arXiv:1403.2232] [INSPIRE].
C. Shen, Z. Qiu and U. Heinz, Shape and flow fluctuations in ultracentral Pb + Pb collisions at the energies available at the CERN Large Hadron Collider, Phys. Rev. C 92 (2015) 014901 [arXiv:1502.04636] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1501.04644
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Chesler, P.M., Yaffe, L.G. Holography and off-center collisions of localized shock waves. J. High Energ. Phys. 2015, 70 (2015). https://doi.org/10.1007/JHEP10(2015)070
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2015)070