Abstract
Using holographic duality, we present results for both head-on and off-center collisions of Gaussian shock waves in strongly coupled \( \mathcal{N}=4 \) supersymmetric Yang-Mills theory. The shock waves superficially resemble Lorentz contracted colliding protons. The collisions results in the formation of a plasma whose evolution is well described by viscous hydrodynamics. The size of the produced droplet is R ∼ 1/T eff where T eff is the effective temperature, which is the characteristic microscopic scale in strongly coupled plasma. These results demonstrate the applicability of hydrodynamics to microscopically small systems and bolster the notion that hydrodynamics can be applied to heavy-light ion collisions as well as some proton-proton collisions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
CMS collaboration, Multiplicity and transverse momentum dependence of two- and four-particle correlations in pPb and PbPb collisions, Phys. Lett. B 724 (2013) 213 [arXiv:1305.0609] [INSPIRE].
ALICE collaboration, Long-range angular correlations on the near and away side in p-Pb collisions at \( \sqrt{s_{NN}}=5.02 \) TeV, Phys. Lett. B 719 (2013) 29 [arXiv:1212.2001] [INSPIRE].
ATLAS collaboration, Observation of Associated Near-Side and Away-Side Long-Range Correlations in \( \sqrt{s_{NN}}=5.02 \) TeV Proton-Lead Collisions with the ATLAS Detector, Phys. Rev. Lett. 110 (2013) 182302 [arXiv:1212.5198] [INSPIRE].
PHENIX collaboration, A. Adare et al., Quadrupole Anisotropy in Dihadron Azimuthal Correlations in Central d + Au Collisions at \( \sqrt{s_{NN}}=200 \) GeV, Phys. Rev. Lett. 111 (2013) 212301 [arXiv:1303.1794] [INSPIRE].
PHENIX collaboration, A. Adare et al., Measurements of elliptic and triangular flow in high-multiplicity 3 He+Au collisions at \( \sqrt{s_{NN}}=200 \) GeV, Phys. Rev. Lett. 115 (2015) 142301 [arXiv:1507.06273] [INSPIRE].
ATLAS collaboration, Observation of long-range elliptic anisotropies in \( \sqrt{s}=13 \) and 2.76 TeV pp collisions with the ATLAS detector, arXiv:1509.04776 [INSPIRE].
P. Bozek, Collective flow in p-Pb and d-Pd collisions at TeV energies, Phys. Rev. C 85 (2012) 014911 [arXiv:1112.0915] [INSPIRE].
P. Bozek and W. Broniowski, Correlations from hydrodynamic flow in p-Pb collisions, Phys. Lett. B 718 (2013) 1557 [arXiv:1211.0845] [INSPIRE].
A. Bzdak, B. Schenke, P. Tribedy and R. Venugopalan, Initial state geometry and the role of hydrodynamics in proton-proton, proton-nucleus and deuteron-nucleus collisions, Phys. Rev. C 87 (2013) 064906 [arXiv:1304.3403] [INSPIRE].
B. Schenke and R. Venugopalan, Eccentric protons? Sensitivity of flow to system size and shape in p + p, p + Pb and Pb + Pb collisions, Phys. Rev. Lett. 113 (2014) 102301 [arXiv:1405.3605] [INSPIRE].
M. Habich, G.A. Miller, P. Romatschke and W. Xiang, A Hydrodynamic Study of p + p Collisions at \( \sqrt{s}=7 \) TeV, arXiv:1512.05354 [INSPIRE].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
D. Grumiller and P. Romatschke, On the collision of two shock waves in AdS 5, JHEP 08 (2008) 027 [arXiv:0803.3226] [INSPIRE].
J.L. Albacete, Y.V. Kovchegov and A. Taliotis, Modeling Heavy Ion Collisions in AdS/CFT, JHEP 07 (2008) 100 [arXiv:0805.2927] [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].
P.M. Chesler, N. Kilbertus and W. van der Schee, Universal hydrodynamic flow in holographic planar shock collisions, JHEP 11 (2015) 135 [arXiv:1507.02548] [INSPIRE].
P.M. Chesler, Colliding shock waves and hydrodynamics in small systems, Phys. Rev. Lett. 115 (2015) 241602 [arXiv:1506.02209] [INSPIRE].
P.M. Chesler and L.G. Yaffe, Holography and off-center collisions of localized shock waves, JHEP 10 (2015) 070 [arXiv:1501.04644] [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].
P. Romatschke, New Developments in Relativistic Viscous Hydrodynamics, Int. J. Mod. Phys. E 19 (2010) 1 [arXiv:0902.3663] [INSPIRE].
S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear Fluid Dynamics from Gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [INSPIRE].
G. Policastro, D.T. Son and A.O. Starinets, The Shear viscosity of strongly coupled N = 4 supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 87 (2001) 081601 [hep-th/0104066] [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].
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].
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, Hydrodynamic Gradient Expansion in Gauge Theory Plasmas, Phys. Rev. Lett. 110 (2013) 211602 [arXiv:1302.0697] [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].
S. Lin and E. Shuryak, Grazing Collisions of Gravitational Shock Waves and Entropy Production in Heavy Ion Collision, Phys. Rev. D 79 (2009) 124015 [arXiv:0902.1508] [INSPIRE].
M.W. Choptuik, Universality and scaling in gravitational collapse of a massless scalar field, Phys. Rev. Lett. 70 (1993) 9 [INSPIRE].
O. Aharony, S. Minwalla and T. Wiseman, Plasma-balls in large-N gauge theories and localized black holes, Class. Quant. Grav. 23 (2006) 2171 [hep-th/0507219] [INSPIRE].
E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].
O. Aharony, J. Marsano, S. Minwalla, K. Papadodimas and M. Van Raamsdonk, The Hagedorn-deconfinement phase transition in weakly coupled large-N gauge theories, Adv. Theor. Math. Phys. 8 (2004) 603 [hep-th/0310285] [INSPIRE].
O. Aharony, J. Marsano, S. Minwalla, K. Papadodimas and M. Van Raamsdonk, A first order deconfinement transition in large-N Yang-Mills theory on a small S 3, Phys. Rev. D 71 (2005) 125018 [hep-th/0502149] [INSPIRE].
R. Gregory and R. Laflamme, Black strings and p-branes are unstable, Phys. Rev. Lett. 70 (1993) 2837 [hep-th/9301052] [INSPIRE].
V.E. Hubeny and M. Rangamani, Unstable horizons, JHEP 05 (2002) 027 [hep-th/0202189] [INSPIRE].
A. Buchel and L. Lehner, Small black holes in AdS 5 × S 5, Class. Quant. Grav. 32 (2015) 145003 [arXiv:1502.01574] [INSPIRE].
Ó.J.C. Dias, J.E. Santos and B. Way, Lumpy AdS5 × S5 black holes and black belts, JHEP 04 (2015) 060 [arXiv:1501.06574] [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: 1601.01583
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. How big are the smallest drops of quark-gluon plasma?. J. High Energ. Phys. 2016, 146 (2016). https://doi.org/10.1007/JHEP03(2016)146
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2016)146