Abstract
Recent studies, using the AdS/CFT correspondence, of the radiation produced by a decaying system or by an accelerated charge in the \( \mathcal{N} \) = 4 supersymmetric Yang-Mills theory, led to a striking result: the ‘supergravity backreaction’, which is supposed to describe the energy density at infinitely strong coupling, yields exactly the same result as at zero coupling, that is, it shows no trace of quantum broadening. We argue that this is not a real property of the radiation at strong coupling, but an artifact of the backreaction calculation, which is unable to faithfully capture the space-time distribution of the radiation. This becomes obvious in the case of a decaying system (‘virtual photon’), for which the backreaction is tantamount to computing a three-point function in the conformal gauge theory, which is independent of the coupling since protected by symmetries. Whereas this non-renormalization property is specific to the conformal \( \mathcal{N} \) = 4 SYM theory, we argue that the failure of the three-point function to provide a local measurement is in fact generic: it holds in any field theory with non-trivial interactions. To properly study a localized distribution, one should rather compute a four-point function, as standard in deep inelastic scattering. We substantiate these considerations with studies of the radiation produced by the decay of a time-like photon at both weak and strong coupling. We show that by computing four-point functions, in perturbation theory at weak coupling and, respectively, from Witten diagrams at strong coupling, one can follow the quantum evolution and thus demonstrate the broadening of the energy distribution. This broadening is slow when the coupling is weak but it proceeds as fast as possible in the limit of a strong coupling.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C. Herzog, A. Karch, P. Kovtun, C. Kozcaz and L. Yaffe, Energy loss of a heavy quark moving through 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 N = 4 Yang-Mills, Phys. Rev. D 74 (2006) 085012 [hep-ph/0605199] [INSPIRE].
H. Liu, K. Rajagopal and U.A. Wiedemann, Calculating the jet quenching parameter from AdS/CFT, Phys. Rev. Lett. 97 (2006) 182301 [hep-ph/0605178] [INSPIRE].
S. Caron-Huot, P. Kovtun, G.D. Moore, A. Starinets and L.G. Yaffe, Photon and dilepton production in supersymmetric Yang-Mills plasma, JHEP 12 (2006) 015 [hep-th/0607237] [INSPIRE].
M. Chernicoff and A. Guijosa, Energy Loss of Gluons, Baryons and k-Quarks in an N = 4 SYM Plasma, JHEP 02 (2007) 084 [hep-th/0611155] [INSPIRE].
Y. Hatta, E. Iancu and A. Mueller, Jet evolution in the N = 4 SYM plasma at strong coupling, JHEP 05 (2008) 037 [arXiv:0803.2481] [INSPIRE].
S.S. Gubser, D.R. Gulotta, S.S. Pufu and F.D. Rocha, Gluon energy loss in the gauge-string duality, JHEP 10 (2008) 052 [arXiv:0803.1470] [INSPIRE].
F. Dominguez, C. Marquet, A. Mueller, B. Wu and B.-W. Xiao, Comparing energy loss and p-perpendicular - broadening in perturbative QCD with strong coupling N = 4 SYM theory, Nucl. Phys. A 811 (2008) 197 [arXiv:0803.3234] [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].
K.B. Fadafan and H. Soltanpanahi, Energy loss in a strongly coupled anisotropic plasma, JHEP 10 (2012) 085 [arXiv:1206.2271] [INSPIRE].
C. Athanasiou, P.M. Chesler, H. Liu, D. Nickel and K. Rajagopal, Synchrotron radiation in strongly coupled conformal field theories, Phys. Rev. D 81 (2010) 126001 [Erratum ibid. D 84 (2011) 069901] [arXiv:1001.3880] [INSPIRE].
Y. Hatta, E. Iancu, A. Mueller and D. Triantafyllopoulos, Aspects of the UV/IR correspondence: energy broadening and string fluctuations, JHEP 02 (2011) 065 [arXiv:1011.3763] [INSPIRE].
Y. Hatta, E. Iancu, A. Mueller and D. Triantafyllopoulos, Radiation by a heavy quark in N =4 SYM at strong coupling, Nucl. Phys. B 850 (2011) 31[arXiv:1102.0232] [INSPIRE].
R. Baier, On radiation by a heavy quark in N = 4 SYM, Adv. High Energy Phys. 2012 (2012) 592854 [arXiv:1107.4250] [INSPIRE].
V.E. Hubeny, Holographic dual of collimated radiation, New J. Phys. 13 (2011) 035006 [arXiv:1012.3561] [INSPIRE].
M. Chernicoff, A. Guijosa and J.F. Pedraza, The Gluonic Field of a Heavy Quark in Conformal Field Theories at Strong Coupling, JHEP 10 (2011) 041 [arXiv:1106.4059] [INSPIRE].
B. Fiol and B. Garolera, Energy Loss of an Infinitely Massive Half-Bogomol’nyi-Prasad-Sommerfeld Particle by Radiation to All Orders in 1/N, Phys. Rev. Lett. 107 (2011) 151601 [arXiv:1106.5418] [INSPIRE].
B. Fiol, B. Garolera and A. Lewkowycz, Exact results for static and radiative fields of a quark in N = 4 super Yang-Mills, JHEP 05 (2012) 093 [arXiv:1202.5292] [INSPIRE].
D. Correa, J. Henn, J. Maldacena and A. Sever, An exact formula for the radiation of a moving quark in N = 4 super Yang-Mills, JHEP 06 (2012) 048 [arXiv:1202.4455] [INSPIRE].
C.A. Agon, A. Guijosa and B.O. Larios, On the Beaming of Gluonic Fields at Strong Coupling, arXiv:1206.5005 [INSPIRE].
D.M. Hofman and J. Maldacena, Conformal collider physics: Energy and charge correlations, JHEP 05 (2008) 012 [arXiv:0803.1467] [INSPIRE].
Y. Hatta and T. Matsuo, Jet fragmentation and gauge/string duality, Phys. Lett. B 670 (2008) 150 [arXiv:0804.4733] [INSPIRE].
Y. Hatta and T. Matsuo, Thermal hadron spectrum in e + e − annihilation from gauge/string duality, Phys. Rev. Lett. 102 (2009) 062001 [arXiv:0807.0098] [INSPIRE].
J. Polchinski and M.J. Strassler, Deep inelastic scattering and gauge/string duality, JHEP 05 (2003) 012 [hep-th/0209211] [INSPIRE].
R.C. Brower, J. Polchinski, M.J. Strassler and C.-I. Tan, The Pomeron and gauge/string duality, JHEP 12 (2007) 005 [hep-th/0603115] [INSPIRE].
C. Ballon Bayona, H. Boschi-Filho and N.R. Braga, Deep inelastic scattering from gauge string duality in the soft wall model, JHEP 03 (2008) 064 [arXiv:0711.0221] [INSPIRE].
Y. Hatta, E. Iancu and A. Mueller, Deep inelastic scattering at strong coupling from gauge/string duality: The Saturation line, JHEP 01 (2008) 026 [arXiv:0710.2148] [INSPIRE].
Y. Hatta, E. Iancu and A. Mueller, Deep inelastic scattering off a N = 4 SYM plasma at strong coupling, JHEP 01 (2008) 063 [arXiv:0710.5297] [INSPIRE].
L. Cornalba and M.S. Costa, Saturation in Deep Inelastic Scattering from AdS/CFT, Phys. Rev. D 78 (2008) 096010 [arXiv:0804.1562] [INSPIRE].
E. Avsar, E. Iancu, L. McLerran and D. Triantafyllopoulos, Shockwaves and deep inelastic scattering within the gauge/gravity duality, JHEP 11 (2009) 105 [arXiv:0907.4604] [INSPIRE].
D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Correlation functions in the CFT(d)/AdS(d + 1) correspondence, Nucl. Phys. B 546 (1999) 96 [hep-th/9804058] [INSPIRE].
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] [INSPIRE].
S.S. Gubser, S.S. Pufu and A. Yarom, Energy disturbances due to a moving quark from gauge-string duality, JHEP 09 (2007) 108 [arXiv:0706.0213] [INSPIRE].
P.M. Chesler and L.G. Yaffe, The Wake of a quark moving through a strongly-coupled plasma, Phys. Rev. Lett. 99 (2007) 152001 [arXiv:0706.0368] [INSPIRE].
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] [INSPIRE].
P.M. Chesler, K. Jensen and A. Karch, Jets in strongly-coupled N = 4 super Yang-Mills theory, Phys. Rev. D 79 (2009) 025021 [arXiv:0804.3110] [INSPIRE].
P. Arnold and D. Vaman, Jet quenching in hot strongly coupled gauge theories revisited: 3-point correlators with gauge-gravity duality, JHEP 10 (2010) 099 [arXiv:1008.4023] [INSPIRE].
P. Arnold and D. Vaman, 4-point correlators in finite-temperature AdS/CFT: Jet quenching correlations, JHEP 11 (2011) 033 [arXiv:1109.0040] [INSPIRE].
P.M. Chesler, Y.-Y. Ho and K. Rajagopal, Shining a Gluon Beam Through quark-gluon Plasma, Phys. Rev. D 85 (2012) 126006 [arXiv:1111.1691] [INSPIRE].
Y. Hatta and T. Ueda, Soft photon anomaly and gauge/string duality, Nucl. Phys. B 837 (2010) 22 [arXiv:1002.3452] [INSPIRE].
A. Mikhailov, Nonlinear waves in AdS/CFT correspondence, hep-th/0305196 [INSPIRE].
E. Buchbinder and A. Tseytlin, Correlation function of circular Wilson loop with two local operators and conformal invariance, arXiv:1208.5138 [INSPIRE].
A.V. Belitsky, G. Korchemsky and G.F. Sterman, Energy flow in QCD and event shape functions, Phys. Lett. B 515 (2001) 297 [hep-ph/0106308] [INSPIRE].
L. Susskind and E. Witten, The Holographic bound in anti-de Sitter space, hep-th/9805114 [INSPIRE].
A.W. Peet and J. Polchinski, UV/IR relations in AdS dynamics, Phys. Rev. D 59 (1999) 065011 [hep-th/9809022] [INSPIRE].
A. Kotikov and L. Lipatov, DGLAP and BFKL equations in the N = 4 supersymmetric gauge theory, Nucl. Phys. B 661 (2003) 19 [Erratum ibid. B 685 (2004) 405] [hep-ph/0208220] [INSPIRE].
D. Binosi and L. Theussl, JaxoDraw: A Graphical user interface for drawing Feynman diagrams, Comput. Phys. Commun. 161 (2004) 76 [hep-ph/0309015] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1210.1534
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Hatta, Y., Iancu, E., Mueller, A.H. et al. Jet evolution from weak to strong coupling. J. High Energ. Phys. 2012, 114 (2012). https://doi.org/10.1007/JHEP12(2012)114
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2012)114