Skip to main content
SpringerLink
Log in

The Gauge-String Duality and Heavy Ion Collisions

  • Published:
Foundations of Physics Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

I review at a non-technical level the use of the gauge-string duality to study aspects of heavy ion collisions, with special emphasis on the trailing string calculation of heavy quark energy loss. I include some brief speculations on how variants of the trailing string construction could provide a toy model of black hole formation and evaporation. This essay is an invited contribution to “Forty Years of String Theory” and is aimed at philosophers and historians of science as well as physicists.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Notes

  1. The remarks quoted in the first two paragraphs come from various sources. “Theory of everything” came to early prominence in [1]. String theory’s development is characterized as backward in [2]. The phrase “string miracles” occurs in [3]. Witten’s remark appeared in print in [4]. Townsend’s quote hasn’t appeared in print as far as I know, and it is more properly understood as the closest paraphrase that my memory can provide. The expression “Not even wrong” is apparently due to Pauli, but its application to string theory is most prominent in [5]. “The Trouble with Physics” is the title of [6]. Wilczek’s quote appeared in [7].

  2. It is striking that early explorations [20] of what became the membrane paradigm of black hole horizons revealed essentially the same result for the shear viscosity as found in [19]. But the interpretation of that early work is obscured by the existence of a negative (and so apparently unphysical) bulk viscosity. Also, the horizons considered in [20] are of finite extent, which obstructs the hydrodynamic limit. In any case, the context of the gauge-string duality, together with the motivation from heavy-ion physics to be explained below, make clear the proper physical interpretation of the result, as well as its importance.

  3. Strictly speaking, the spin 1 particles of \({\mathcal{N}}=4\) super-Yang-Mills theory are generalized gluons, in the sense that physically observed gluons are particles associated with the SU(3) gauge symmetry of QCD, whereas the gluons of \({\mathcal{N}}=4\) super-Yang-Mills are associated with an SU(N) gauge invariance, with N arbitrary at this stage.

  4. Collisions of protons on protons are also common, and the LHC focuses on this type of collision.

  5. Nevertheless there is a robust effort to describe many facets of the initial state and early stages of the collision using a combination of perturbative and semi-classical methods. In addition to [26], see for example the reviews [27, 28].

  6. I would be remiss not to note that there are QCD calculations, both in perturbative and partially perturbative frameworks, which have made impressive headway on the problem of describing rapid energy loss. For an introductory review of these methods, see for example [36].

  7. Viscosity also relates to a time-dependent situation, where a fluid has some non-trivial motion (shearing flow, for example) which damps out over time at a rate that the viscosity controls. For viscosity (as well as other transport properties) a standard approach is to extract an appropriate transport coefficient from a two-point correlator, which represents a perturbation of a uniform, static system. In principle, lattice QCD practitioners can get at the appropriate two-point functions, and the effort to do so for viscosity has had some success [47]. So the point is not that lattice QCD cannot possibly get at the quantities that string theorists compute; rather, it’s that string theorists have, at least temporarily, the advantage of a simpler and more nearly analytically tractable approach.

  8. The sense in which this must happen is that signals on the parts of the worldsheet where v(r)<v 0 have no choice but to propagate further away from the string endpoint. This is a simple version of the notion of an apparent horizon.

  9. There is a significant caveat to this statement: one could imagine a situation where for arbitrarily late times, there is always some part of the string worldsheet, however small it may be, which cannot send a signal to the endpoint of the string. Such a situation would be like a black hole remnant. To rule out such a possibility, one could impose the constraint that the string ends on a brane which is deep down in the bulk.

References

  1. Ellis, J.: The superstring: theory of everything, or of nothing? Nature 323, 595–598 (1986)

    Article  ADS  Google Scholar 

  2. Kaku, M.: Parallel Worlds: A Journey Through Creation, Higher Dimensions, and the Future of the Cosmos. Doubleday, New York (2005)

    Google Scholar 

  3. Dine, M., Seiberg, N.: Are (0, 2) models string miracles? Nucl. Phys. B 306, 137–159 (1988)

    Article  MathSciNet  ADS  Google Scholar 

  4. Lemonick, M.: Edward Witten. Time Mag. (April, 2004)

  5. Woit, P.: Not Even Wrong: The Failure of String Theory, the Continuing Challenge to Unify the Laws of Physics. Basic Books, New York (2006)

    Google Scholar 

  6. Smolin, L.: The Trouble with Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next. Houghton Mifflin, Boston (2006)

    MATH  Google Scholar 

  7. The Nobel Prize and after: a talk with Frank Wilczek. http://www.edge.org/3rd_culture/wilczek09/wilczek09_index.html

  8. Maldacena, J.M.: The large N limit of superconformal field theories and supergravity. Adv. Theor. Math. Phys. 2, 231–252 (1998). hep-th/9711200

    MathSciNet  ADS  MATH  Google Scholar 

  9. Gubser, S.S., Klebanov, I.R., Polyakov, A.M.: Gauge theory correlators from non-critical string theory. Phys. Lett. B 428, 105–114 (1998). hep-th/9802109

    Article  MathSciNet  ADS  Google Scholar 

  10. Witten, E.: Anti-de Sitter space and holography. Adv. Theor. Math. Phys. 2, 253–291 (1998). hep-th/9802150

    MathSciNet  ADS  MATH  Google Scholar 

  11. Townsend, P.: The eleven-dimensional supermembrane revisited. Phys. Lett. B 350, 184–187 (1995). hep-th/9501068

    Article  MathSciNet  ADS  Google Scholar 

  12. Witten, E.: String theory dynamics in various dimensions. Nucl. Phys. B 443, 85–126 (1995). hep-th/9503124

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. Strominger, A., Vafa, C.: Microscopic origin of the Bekenstein-Hawking entropy. Phys. Lett. B 379, 99–104 (1996). hep-th/9601029

    Article  MathSciNet  ADS  Google Scholar 

  14. Polchinski, J.: Dirichlet-branes and Ramond-Ramond charges. Phys. Rev. Lett. 75, 4724–4727 (1995). hep-th/9510017

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. Das, S.R., Mathur, S.D.: Comparing decay rates for black holes and D-branes. Nucl. Phys. B 478, 561–576 (1996). hep-th/9606185

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. ’t Hooft, G.: Dimensional reduction in quantum gravity. gr-qc/9310026. Essay dedicated to Abdus Salam

  17. Susskind, L.: The World as a hologram. J. Math. Phys. 36, 6377–6396 (1995). hep-th/9409089

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. Thorne, K.S., Price, R., Macdonald, D. (eds.): Black Holes: the Membrane Paradigm. Yale University Press, New York (1986)

    Google Scholar 

  19. Policastro, G., Son, D.T., Starinets, A.O.: The shear viscosity of strongly coupled N=4 supersymmetric Yang-Mills plasma. Phys. Rev. Lett. 87, 081601 (2001). hep-th/0104066

    Article  ADS  Google Scholar 

  20. Damour, T.: Surface effects in black-hole physics. In: Ruffini, R. (ed.) Proceedings of the Second Marcel Grossmann Meeting on General Relativity, p. 587. North-Holland, Amsterdam (1982)

    Google Scholar 

  21. Butler, S.: High-energy physics made painless. Fermi News 20, 5 (1997)

    Google Scholar 

  22. Adcox, K., et al. (PHENIX Collaboration): Formation of dense partonic matter in relativistic nucleus-nucleus collisions at RHIC: Experimental evaluation by the PHENIX collaboration. Nucl. Phys. A 757, 184–283 (2005). nucl-ex/0410003

    Article  ADS  Google Scholar 

  23. Arsene, I., et al. (BRAHMS Collaboration): Quark gluon plasma and color glass condensate at RHIC? The perspective from the BRAHMS experiment. Nucl. Phys. A 757, 1–27 (2005). nucl-ex/0410020

    Article  ADS  Google Scholar 

  24. Back, B.B., et al.: The PHOBOS perspective on discoveries at RHIC. Nucl. Phys. A 757, 28–101 (2005). nucl-ex/0410022

    Article  ADS  Google Scholar 

  25. Adams, J., et al. (STAR Collaboration): 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, 102–183 (2005). nucl-ex/0501009

    Article  ADS  Google Scholar 

  26. Abreu, S., et al.: Heavy ion collisions at the LHC—last call for predictions. J. Phys. G 35, 054001 (2008). 0711.0974. Edited by N. Armesto, N. Borghini, S. Jeon, and U.A. Wiedemann

    Article  MathSciNet  Google Scholar 

  27. McLerran, L.: The color glass condensate and glasma. 0804.1736

  28. Gelis, F., Iancu, E., Jalilian-Marian, J., Venugopalan, R.: The color glass condensate. 1002.0333

  29. Heinz, U.W.: Concepts of heavy-ion physics. hep-ph/0407360

  30. Bohr, N., Wheeler, J.A.: The mechanism of nuclear fission. Phys. Rev. 56, 426–450 (1939)

    Article  ADS  Google Scholar 

  31. Adare, A., et al. (PHENIX Collaboration): Detailed measurement of the e + e − pair continuum in p+p and Au+Au collisions at \(\sqrt{s_{NN}} = 200~\mathrm{GeV}\) and implications for direct photon production. Phys. Rev. C 81, 034911 (2010). 0912.0244

    Article  ADS  Google Scholar 

  32. Gubser, S.S., Klebanov, I.R., Peet, A.W.: Entropy and temperature of black 3-branes. Phys. Rev. D 54, 3915–3919 (1996). hep-th/9602135

    Article  MathSciNet  ADS  Google Scholar 

  33. Luzum, M., Romatschke, P.: Conformal relativistic viscous hydrodynamics: applications to RHIC results at \(\sqrt{s_{NN}} = 200~\mathrm{GeV}\). Phys. Rev. C 78, 034915 (2008). 0804.4015

    Article  ADS  Google Scholar 

  34. Arnold, P.B., Moore, G.D., Yaffe, L.G.: Transport coefficients in high temperature gauge theories: (I) Leading-log results. J. High Energy Phys. 11, 001 (2000). hep-ph/0010177

    Article  ADS  Google Scholar 

  35. Kovtun, P., Son, D.T., Starinets, A.O.: Viscosity in strongly interacting quantum field theories from black hole physics. Phys. Rev. Lett. 94, 111601 (2005). hep-th/0405231

    Article  ADS  Google Scholar 

  36. Casalderrey-Solana, J., Salgado, C.A.: Introductory lectures on jet quenching in heavy ion collisions. Acta Phys. Pol. B 38, 3731–3794 (2007). 0712.3443

    ADS  Google Scholar 

  37. Liu, H., Rajagopal, K., Wiedemann, U.A.: Calculating the jet quenching parameter from AdS/CFT. Phys. Rev. Lett. 97, 182301 (2006). hep-ph/0605178

    Article  ADS  Google Scholar 

  38. Herzog, C.P., Karch, A., Kovtun, P., Kozcaz, C., Yaffe, L.G.: Energy loss of a heavy quark moving through N=4 supersymmetric Yang-Mills plasma. J. High Energy Phys. 07, 013 (2006). hep-th/0605158

    Article  MathSciNet  ADS  Google Scholar 

  39. Casalderrey-Solana, J., Teaney, D.: Heavy quark diffusion in strongly coupled \({\mathcal{N}} = 4\) Yang-Mills. Phys. Rev. D 74, 085012 (2006). hep-ph/0605199

    Article  ADS  Google Scholar 

  40. Gubser, S.S.: Drag force in AdS/CFT. Phys. Rev. D 74, 126005 (2006). hep-th/0605182

    Article  MathSciNet  ADS  Google Scholar 

  41. Akamatsu, Y., Hatsuda, T., Hirano, T.: Heavy quark diffusion with relativistic Langevin dynamics in the quark-gluon fluid. Phys. Rev. C 79, 054907 (2009). 0809.1499

    Article  ADS  Google Scholar 

  42. Gubser, S.S., Yarom, A.: Pointlike probes of superstring-theoretic superfluids. J. High Energy Phys. 1003, 041 (2010). 0908.1392

    Article  MathSciNet  ADS  Google Scholar 

  43. Rey, S.-J., Yee, J.-T.: Macroscopic strings as heavy quarks in large N gauge theory and anti-de Sitter supergravity. Eur. Phys. J. C 22, 379–394 (2001). hep-th/9803001

    Article  MathSciNet  ADS  MATH  Google Scholar 

  44. Maldacena, J.M.: Wilson loops in large N field theories. Phys. Rev. Lett. 80, 4859–4862 (1998). hep-th/9803002

    Article  MathSciNet  ADS  MATH  Google Scholar 

  45. Karsch, F.: Properties of the quark gluon plasma: a lattice perspective. Nucl. Phys. A 783, 13–22 (2007). hep-ph/0610024

    Article  ADS  Google Scholar 

  46. Gubser, S.S.: Comparing the drag force on heavy quarks in N=4 super-Yang-Mills theory and QCD. Phys. Rev. D 76, 126003 (2007). hep-th/0611272

    Article  ADS  Google Scholar 

  47. Meyer, H.B.: A calculation of the shear viscosity in SU(3) gluodynamics. Phys. Rev. D 76, 101701 (2007). 0704.1801

    Article  ADS  Google Scholar 

  48. Gubser, S.S.: Momentum fluctuations of heavy quarks in the gauge-string duality. Nucl. Phys. B 790, 175–199 (2008). hep-th/0612143

    Article  MathSciNet  ADS  MATH  Google Scholar 

  49. Casalderrey-Solana, J., Teaney, D.: Transverse momentum broadening of a fast quark in a N=4 Yang-Mills plasma. hep-th/0701123

  50. Gubser, S.S., Herzog, C.P., Pufu, S.S., Tesileanu, T.: Superconductors from superstrings. Phys. Rev. Lett. 103, 141601 (2009). 0907.3510

    Article  MathSciNet  ADS  Google Scholar 

  51. Gubser, S.S., Karch, A.: From gauge-string duality to strong interactions: a pedestrian’s guide. Annu. Rev. Nucl. Part. Sci. 59, 145–168 (2009). 0901.0935

    Article  ADS  Google Scholar 

  52. Casalderrey-Solana, J., Liu, H., Mateos, D., Rajagopal, K., Wiedemann, U.A.: Gauge/string duality, hot QCD and heavy ion collisions. 1101.0618

  53. Chesler, P.M., Yaffe, L.G.: Holography and colliding gravitational shock waves in asymptotically AdS 5 spacetime. Phys. Rev. Lett. 106, 021601 (2011). 1011.3562

    Article  ADS  Google Scholar 

  54. Gubser, S.S.: Symmetry constraints on generalizations of Bjorken flow. Phys. Rev. D 82, 085027 (2010). 1006.0006

    Article  MathSciNet  ADS  Google Scholar 

  55. Gubser, S.S., Yarom, A.: Conformal hydrodynamics in Minkowski and de Sitter spacetimes. Nucl. Phys. B 846, 469–511 (2011). 1012.1314

    Article  MathSciNet  ADS  MATH  Google Scholar 

  56. Gubser, S.S.: Conformal symmetry and the Balitsky-Kovchegov equation. 1102.4040

Download references

Author information

Authors and Affiliations

  1. Joseph Henry Laboratories, Princeton University, Princeton, NJ, 08544, USA

    Steven S. Gubser

Authors
  1. Steven S. Gubser
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Steven S. Gubser.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gubser, S.S. The Gauge-String Duality and Heavy Ion Collisions. Found Phys 43, 140–155 (2013). https://doi.org/10.1007/s10701-011-9613-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10701-011-9613-9

Keywords

Search

Navigation