Abstract
Using AdS/CFT we investigate the effect of angular-momentum-induced anisotropy on the instantaneous drag force of a heavy quark. The dual description is that of a string moving in the background of a Kerr-AdS black hole. The system exhibits the expected focusing of jets towards the impact parameter plane. We put forward that we can use the connection between this focusing behavior and the angular momentum induced pressure gradient to extrapolate the pressure gradient correction to the drag force that can be used for transverse elliptic flow in realistic heavy ion collisions. The result is recognizable as a relativistic pressure gradient force.
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References
E.V. Shuryak, Strongly coupled quark-gluon plasma: The status report, hep-ph/0608177 [SPIRES].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [SPIRES].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [SPIRES].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [SPIRES].
E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505[hep-th/9803131] [SPIRES].
S.S. Gubser, Drag force in AdS/CFT, Phys. Rev. D 74 (2006) 126005 [hep-th/0605182] [SPIRES].
S. Bhattacharyya, S. Lahiri, R. Loganayagam and S. Minwalla, Large rotating AdS black holes from fluid mechanics, JHEP 09 (2008) 054 [arXiv:0708.1770] [SPIRES].
D.T. Son and A.O. Starinets, Viscosity, Black Holes and Quantum Field Theory, Ann. Rev. Nucl. Part. Sci. 57 (2007) 95 [arXiv:0704.0240] [SPIRES].
P.F. Kolb, J. Sollfrank and U.W. Heinz, Anisotropic transverse flow and the quark-hadron phase transition, Phys. Rev. C 62 (2000) 054909 [hep-ph/0006129] [SPIRES].
P.F. Kolb, P. Huovinen, U.W. Heinz and H. Heiselberg, Elliptic flow at SPS and RHIC: From kinetic transport to hydrodynamics, Phys. Lett. B 500 (2001) 232 [hep-ph/0012137] [SPIRES].
P.F. Kolb and U.W. Heinz, Hydrodynamic description of ultrarelativistic heavy-ion collisions, nucl-th/0305084 [SPIRES].
S. Bhattacharyya et al., Local Fluid Dynamical Entropy from Gravity, JHEP 06 (2008) 055 [arXiv:0803.2526] [SPIRES].
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] [SPIRES].
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] [SPIRES].
S.S. Gubser, S.S. Pufu and A. Yarom, Off-center collisions in AdS 5 with applications to multiplicity estimates in heavy-ion collisions, JHEP 11 (2009) 050 [arXiv:0902.4062] [SPIRES].
E. Avsar, E. Iancu, L. McLerran and D.N. Triantafyllopoulos, Shockwaves and deep inelastic scattering within the gauge/gravity duality, JHEP 11 (2009) 105 [arXiv:0907.4604] [SPIRES].
A. Duenas-Vidal and M.A. Vazquez-Mozo, Colliding AdS gravitational shock waves in various dimensions and holography, JHEP 07 (2010) 021 [arXiv:1004.2609] [SPIRES].
A. Taliotis, Heavy Ion Collisions with Transverse Dynamics from Evolving AdS Geometries, JHEP 09 (2010) 102 [arXiv:1004.3500] [SPIRES].
J.M. Maldacena, Wilson loops in large-N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [SPIRES].
S.-J. Rey, S. Theisen and J.-T. Yee, Wilson-Polyakov loop at finite temperature in large-N gauge theory and anti-de Sitter supergravity, Nucl. Phys. B 527 (1998) 171 [hep-th/9803135] [SPIRES].
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] [SPIRES].
C.P. Herzog, A. Karch, P. Kovtun, C. Kozcaz and L.G. Yaffe, Energy loss of a heavy quark moving through N = 4 supersymmetric Yang-Mills plasma, JHEP 07 (2006) 013 [hep-th/0605158] [SPIRES].
P.M. Chesler and L.G. Yaffe, The wake of a quark moving through a strongly-coupled \( \mathcal{N} = 4 \) supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 99 (2007) 152001 [arXiv:0706.0368] [SPIRES].
P.M. Chesler and L.G. Yaffe, The stress-energy tensor of a quark moving through a strongly-coupled N = 4 supersymmetric Yang-Mills plasma: comparing hydrodynamics and AdS/CFT, Phys. Rev. D 78 (2008) 045013 [arXiv:0712.0050] [SPIRES].
J.J. Friess, S.S. Gubser and G. Michalogiorgakis, Dissipation from a heavy quark moving through N = 4 super-Yang-Mills plasma, JHEP 09 (2006) 072 [hep-th/0605292] [SPIRES].
J.J. Friess, S.S. Gubser, G. Michalogiorgakis and S.S. Pufu, The stress tensor of a quark moving through N = 4 thermal plasma, Phys. Rev. D 75 (2007) 106003 [hep-th/0607022] [SPIRES].
J.J. Friess, S.S. Gubser, G. Michalogiorgakis and S.S. Pufu, Expanding plasmas and quasinormal modes of anti-de Sitter black holes, JHEP 04 (2007) 080 [hep-th/0611005] [SPIRES].
S.A. Voloshin, A.M. Poskanzer and R. Snellings, Collective phenomena in non-central nuclear collisions, arXiv:0809.2949 [SPIRES].
F. Becattini, F. Piccinini and J. Rizzo, Angular momentum conservation in heavy ion collisions at very high energy, Phys. Rev. C 77 (2008) 024906 [arXiv:0711.1253] [SPIRES].
N. Armesto, (ed.) et al., Heavy Ion Collisions at the LHC-Last Call for Predictions, J. Phys. G 35 (2008) 054001 [arXiv:0711.0974] [SPIRES].
S. Hemming and L. Thorlacius, Thermodynamics of Large AdS Black Holes, JHEP 11 (2007) 086 [arXiv:0709.3738] [SPIRES].
M. Henneaux and C. Teitelboim, Asymptotically anti-de Sitter Spaces, Commun. Math. Phys. 98 (1985) 391 [SPIRES].
S.W. Hawking, C.J. Hunter and M. Taylor, Rotation and the AdS/CFT correspondence, Phys. Rev. D 59 (1999) 064005 [hep-th/9811056] [SPIRES].
J. de Boer, V.E. Hubeny, M. Rangamani and M. Shigemori, Brownian motion in AdS/CFT, JHEP 07 (2009) 094 [arXiv:0812.5112] [SPIRES].
G.W. Gibbons, M.J. Perry and C.N. Pope, The First Law of Thermodynamics for Kerr-Anti-de Sitter Black Holes, Class. Quant. Grav. 22 (2005) 1503 [hep-th/0408217] [SPIRES].
G.W. Gibbons, H. Lü, D.N. Page and C.N. Pope, The general Kerr-de Sitter metrics in all dimensions, J. Geom. Phys. 53 (2005) 49 [hep-th/0404008] [SPIRES].
C.P. Herzog, Energy loss of heavy quarks from asymptotically AdS geometries, JHEP 09 (2006) 032 [hep-th/0605191] [SPIRES].
E. Caceres and A. Guijosa, Drag force in charged N = 4 SYM plasma, JHEP 11 (2006) 077 [hep-th/0605235] [SPIRES].
C.P. Herzog and A. Vuorinen, Spinning Dragging Strings, JHEP 10 (2007) 087 [arXiv:0708.0609] [SPIRES].
A.N. Atmaja, J. de Boer and M. Shigemori, Holographic Brownian Motion and Time Scales in Strongly Coupled Plasmas, arXiv:1002.2429 [SPIRES].
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Nata Atmaja, A., Schalm, K. Anisotropic drag force from 4D Kerr-AdS black hole. J. High Energ. Phys. 2011, 70 (2011). https://doi.org/10.1007/JHEP04(2011)070
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DOI: https://doi.org/10.1007/JHEP04(2011)070