Abstract
We calculate the drag force experienced by an infinitely massive quark propagating at constant velocity through an anisotropic, strongly coupled \( \mathcal{N} = 4 \) plasma by means of its gravity dual. We find that the gluon cloud trailing behind the quark is generally misaligned with the quark velocity, and that the latter is also misaligned with the force. The drag coefficient μ can be larger or smaller than the corresponding isotropic value depending on the velocity and the direction of motion. In the ultra-relativistic limit we find that generically μ ∝ p. We discuss the conditions under which this behaviour may extend to more general situations.
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References
STAR collaboration, J. Adams et al., Experimental and theoretical challenges in the search for the quark gluon plasma: the STAR collaboration’s critical assessment of the evidence from RHIC collisions, Nucl. Phys. A 757 (2005) 102 [nucl-ex/0501009] [INSPIRE].
PHENIX collaboration, K. Adcox et al., Formation of dense partonic matter in relativistic nucleus-nucleus collisions at RHIC: experimental evaluation by the PHENIX collaboration, Nucl. Phys. A 757 (2005) 184 [nucl-ex/0410003] [INSPIRE].
Proceedings of the Quark Matter 2011, J. Phys. G 38 (2011) 120301.
E. Shuryak, Why does the quark gluon plasma at RHIC behave as a nearly ideal fluid?, Prog. Part. Nucl. Phys. 53 (2004) 273 [hep-ph/0312227] [INSPIRE].
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].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113 ] [hep-th/9711200] [INSPIRE].
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].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal and U.A. Wiedemann, Gauge/string duality, hot QCD and heavy ion collisions, arXiv:1101.0618 [INSPIRE].
W. Florkowski, Anisotropic fluid dynamics in the early stage of relativistic heavy-ion collisions, Phys. Lett. B 668 (2008) 32 [arXiv:0806.2268] [INSPIRE].
W. Florkowski and R. Ryblewski, Dynamics of anisotropic plasma at the early stages of relativistic heavy-ion collisions, Acta Phys. Polon. B 40 (2009) 2843 [arXiv:0901.4653] [INSPIRE].
R. Ryblewski and W. Florkowski, Early anisotropic hydrodynamics and the RHIC early-thermalization and HBT puzzles, Phys. Rev. C 82 (2010) 024903 [arXiv:1004.1594] [INSPIRE].
W. Florkowski and R. Ryblewski, Highly-anisotropic and strongly-dissipative hydrodynamics for early stages of relativistic heavy-ion collisions, Phys. Rev. C 83 (2011) 034907 [arXiv:1007.0130] [INSPIRE].
M. Martinez and M. Strickland, Dissipative dynamics of highly anisotropic systems, Nucl. Phys. A 848 (2010) 183 [arXiv:1007.0889] [INSPIRE].
R. Ryblewski and W. Florkowski, Non-boost-invariant motion of dissipative and highly anisotropic fluid, J. Phys. G 38 (2011) 015104 [arXiv:1007.4662] [INSPIRE].
M. Martinez and M. Strickland, Non-boost-invariant anisotropic dynamics, Nucl. Phys. A 856 (2011) 68 [arXiv:1011.3056] [INSPIRE].
R. Ryblewski and W. Florkowski, Highly anisotropic hydrodynamics — discussion of the model assumptions and forms of the initial conditions, Acta Phys. Polon. B 42 (2011) 115 [arXiv:1011.6213] [INSPIRE].
R. Ryblewski and W. Florkowski, Highly-anisotropic and strongly-dissipative hydrodynamics with transverse expansion, Eur. Phys. J. C 71 (2011) 1761 [arXiv:1103.1260] [INSPIRE].
D. Mateos and D. Trancanelli, The anisotropic \( \mathcal{N} = 4 \) super Yang-Mills plasma and its instabilities, Phys. Rev. Lett. 107 (2011) 101601 [arXiv:1105.3472] [INSPIRE].
D. Mateos and D. Trancanelli, Thermodynamics and instabilities of a strongly coupled anisotropic plasma, JHEP 07 (2011) 054 [arXiv:1106.1637] [INSPIRE].
C. Herzog, A. Karch, P. Kovtun, C. Kozcaz and L. Yaffe, Energy loss of a heavy quark moving through \( \mathcal{N} = 4 \) supersymmetric Yang-Mills plasma, JHEP 07 (2006) 013 [hep-th/0605158] [INSPIRE].
S.S. Gubser, Drag force in AdS/CFT, Phys. Rev. D 74 (2006) 126005 [hep-th/0605182] [INSPIRE].
J. Casalderrey-Solana and D. Teaney, Heavy quark diffusion in strongly coupled \( \mathcal{N} = 4 \) Yang-Mills, Phys. Rev. D 74 (2006) 085012 [hep-ph/0605199] [INSPIRE].
C.P. Herzog, Energy loss of heavy quarks from asymptotically AdS geometries, JHEP 09 (2006) 032 [hep-th/0605191] [INSPIRE].
E. Caceres and A. Guijosa, Drag force in charged \( \mathcal{N} = 4 \) SYM plasma, JHEP 11 (2006) 077 [hep-th/0605235] [INSPIRE].
S.-J. Sin and I. Zahed, Ampere’s law and energy loss in AdS/CFT duality, Phys. Lett. B 648 (2007) 318 [hep-ph/0606049] [INSPIRE].
T. Matsuo, D. Tomino and W.-Y. Wen, Drag force in SYM plasma with B field from AdS/CFT, JHEP 10 (2006) 055 [hep-th/0607178] [INSPIRE].
P. Talavera, Drag force in a string model dual to large-N QCD, JHEP 01 (2007) 086 [hep-th/0610179] [INSPIRE].
E. Antonyan, Friction coefficient for quarks in supergravity duals, hep-th/0611235 [INSPIRE].
A. Karch and A. O’Bannon, Metallic AdS/CFT, JHEP 09 (2007) 024 [arXiv:0705.3870] [INSPIRE].
C. Herzog and A. Vuorinen, Spinning dragging strings, JHEP 10 (2007) 087 [arXiv:0708.0609] [INSPIRE].
M. Chernicoff and A. Guijosa, Energy loss of gluons, baryons and k-quarks in an \( \mathcal{N} = 4 \) SYM plasma, JHEP 02 (2007) 084 [hep-th/0611155] [INSPIRE].
S.S. Gubser, Momentum fluctuations of heavy quarks in the gauge-string duality, Nucl. Phys. B 790 (2008) 175 [hep-th/0612143] [INSPIRE].
J. Casalderrey-Solana and D. Teaney, Transverse momentum broadening of a fast quark in a \( \mathcal{N} = 4 \) Yang-Mills plasma, JHEP 04 (2007) 039 [hep-th/0701123] [INSPIRE].
G. Bertoldi, F. Bigazzi, A.L. Cotrone and J.D. Edelstein, Holography and unquenched quark-gluon plasmas, Phys. Rev. D 76 (2007) 065007 [hep-th/0702225] [INSPIRE].
K.B. Fadafan, R 2 curvature-squared corrections on drag force, JHEP 12 (2008) 051 [arXiv:0803.2777] [INSPIRE].
M. Chernicoff and A. Guijosa, Acceleration, energy loss and screening in strongly-coupled gauge theories, JHEP 06 (2008) 005 [arXiv:0803.3070] [INSPIRE].
K.B. Fadafan, Charge effect and finite ’t Hooft coupling correction on drag force and jet quenching parameter, Eur. Phys. J. C 68 (2010) 505 [arXiv:0809.1336] [INSPIRE].
F. Bigazzi, A.L. Cotrone, J. Mas, A. Paredes, A.V. Ramallo and J. Tarrío, D3-D7 quark-gluon plasmas, JHEP 11 (2009) 117 [arXiv:0909.2865] [INSPIRE].
K.B. Fadafan, Heavy quarks in the presence of higher derivative corrections from AdS/CFT, Eur. Phys. J. C 71 (2011) 1799 [arXiv:1102.2289] [INSPIRE].
A. Guijosa and J.F. Pedraza, Early-time energy loss in a strongly-coupled SYM plasma, JHEP 05 (2011) 108 [arXiv:1102.4893] [INSPIRE].
P. Chesler and A. Vuorinen, Heavy flavor diffusion in weakly coupled \( \mathcal{N} = 4 \) super Yang-Mills theory, JHEP 11 (2006) 037 [hep-ph/0607148] [INSPIRE].
S.C. Huot, S. Jeon and G.D. Moore, Shear viscosity in weakly coupled \( \mathcal{N} = 4 \) super Yang-Mills theory compared to QCD, Phys. Rev. Lett. 98 (2007) 172303 [hep-ph/0608062] [INSPIRE].
J.-P. Blaizot, E. Iancu, U. Kraemmer and A. Rebhan, Hard thermal loops and the entropy of supersymmetric Yang-Mills theories, JHEP 06 (2007) 035 [hep-ph/0611393] [INSPIRE].
W. Horowitz and M. Gyulassy, Heavy quark jet tomography of Pb + Pb at LHC: AdS/CFT drag or pQCD energy loss?, Phys. Lett. B 666 (2008) 320 [arXiv:0706.2336] [INSPIRE].
J.J. Friess, S.S. Gubser and G. Michalogiorgakis, Dissipation from a heavy quark moving through script \( \mathcal{N} = 4 \) super-Yang-Mills plasma, JHEP 09 (2006) 072 [hep-th/0605292] [INSPIRE].
Y.-H. Gao, W.-S. Xu and D.-F. Zeng, Wake of color fields in charged \( \mathcal{N} = 4 \) SYM plasmas, hep-th/0606266 [INSPIRE].
J.J. Friess, S.S. Gubser, G. Michalogiorgakis and S.S. Pufu, Stress tensor of a quark moving through \( \mathcal{N} = 4 \) thermal plasma, Phys. Rev. D 75 (2007) 106003 [hep-th/0607022] [INSPIRE].
A. Yarom, High momentum behavior of a quark wake, Phys. Rev. D 75 (2007) 125010 [hep-th/0702164] [INSPIRE].
A. Yarom, Energy deposited by a quark moving in an \( \mathcal{N} = 4 \) super Yang-Mills plasma, Phys. Rev. D 75 (2007) 105023 [hep-th/0703095] [INSPIRE].
P.M. Chesler and L.G. Yaffe, 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] [INSPIRE].
S.S. Gubser, S.S. Pufu and A. Yarom, Sonic booms and diffusion wakes generated by a heavy quark in thermal gauge-string duality, Phys. Rev. Lett. 100 (2008) 012301 [arXiv:0706.4307] [INSPIRE].
S.S. Gubser and A. Yarom, Universality of the diffusion wake in the gauge-string duality, Phys. Rev. D 77 (2008) 066007 [arXiv:0709.1089] [INSPIRE].
A. Nata Atmaja and K. Schalm, Anisotropic drag force from 4D Kerr-AdS black hole, JHEP 04 (2011) 070 [arXiv:1012.3800] [INSPIRE].
K.L. Panigrahi and S. Roy, Drag force in a hot non-relativistic, non-commutative Yang-Mills plasma, JHEP 04 (2010) 003 [arXiv:1001.2904] [INSPIRE].
T. Azeyanagi, W. Li and T. Takayanagi, On string theory duals of Lifshitz-like fixed points, JHEP 06 (2009) 084 [arXiv:0905.0688] [INSPIRE].
D.Z. Freedman, S.S. Gubser, K. Pilch and N.P. Warner, Renormalization group flows from holography-supersymmetry and a c-theorem, Adv. Theor. Math. Phys. 3 (1999) 363 [hep-th/9904017] [INSPIRE].
K. Pilch and N.P. Warner, \( \mathcal{N} = 2 \) supersymmetric RG flows and the IIB dilaton, Nucl. Phys. B 594 (2001) 209 [hep-th/0004063] [INSPIRE].
A. Buchel and J.T. Liu, Thermodynamics of the \( \mathcal{N} = {2^* } \) flow, JHEP 11 (2003) 031 [hep-th/0305064] [INSPIRE].
A. Karch, E. Katz, D.T. Son and M.A. Stephanov, Linear confinement and AdS/QCD, Phys. Rev. D 74 (2006) 015005 [hep-ph/0602229] [INSPIRE].
C.P. Herzog, Holographic prediction for the deconfinement temperature, Phys. Rev. Lett. 98 (2007) 091601 [hep-th/0608151] [INSPIRE].
E. Nakano, S. Teraguchi and W.-Y. Wen, Drag force, jet quenching and an AdS/QCD model, Phys. Rev. D 75 (2007) 085016 [hep-ph/0608274] [INSPIRE].
C. Hoyos, Drag and jet quenching of heavy quarks in a strongly coupled script \( \mathcal{N} = {2^* } \) plasma, JHEP 09 (2009) 068 [arXiv:0907.5036] [INSPIRE].
H. Liu, K. Rajagopal and Y. Shi, Robustness and infrared sensitivity of various observables in the application of AdS/CFT to heavy ion collisions, JHEP 08 (2008) 048 [arXiv:0803.3214] [INSPIRE].
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Chernicoff, M., Fernández, D., Mateos, D. et al. Drag force in a strongly coupled anisotropic plasma. J. High Energ. Phys. 2012, 100 (2012). https://doi.org/10.1007/JHEP08(2012)100
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DOI: https://doi.org/10.1007/JHEP08(2012)100