Skip to main content
SpringerLink
Log in

In Search of the QCD–Gravity Correspondence

  • Chapter
  • First Online:
The Physics of the Quark-Gluon Plasma

Part of the book series: Lecture Notes in Physics ((LNP,volume 785))

Abstract

Quantum chromodynamics (QCD) is the fundamental theory of strong interactions. It describes the behavior of quarks and gluons which are the smallest known constituents of nuclear matter. The difficulties in solving the theory at low energies in the strongly interacting, non-perturbative regime have left unanswered many important questions in QCD, such as the nature of confinement or the mechanism of hadronization. In these lectures oriented toward the students we introduce two classes of dualities that attempt to reproduce many of the features of QCD, while making the treatment at strong coupling more tractable: (1) the AdS/CFT correspondence between a specific class of string theories and a conformal field theory and (2) an effective low-energy theory of QCD dual to classical QCD on a curved conformal gravitational background. The hope is that by applying these dualities to the evaluation of various properties of the strongly interacting matter produced in heavy-ion collisions, one can understand how QCD behaves at strong coupling. We give an outline of the applications, with emphasis on two transport coefficients of QCD matter – shear and bulk viscosities.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. Maldacena: The Large N Limit of Superconformal Field Theories and Supergravity, Adv. Theor. Math. Phys. 2, 231–252 (1998), arXiv:hep-th/9711200

    MATH  MathSciNet  ADS  Google Scholar 

  2. S. Gubser, I. Klebanov and A. Polyakov: Gauge Theory Correlators from Non-critical String Theory, Phys. Lett. B 428, 105–114 (1998), arXiv:hep-th/9802109

    MathSciNet  ADS  Google Scholar 

  3. E. Witten: Anti-de Sitter Space, Thermal Phase Transition, and Confinement in Gauge Theories, Adv. Theor. Math. Phys. 2, 505–532 (1998), arXiv:hepth/9803131

    MATH  MathSciNet  Google Scholar 

  4. E. Shuryak: Physics of Strongly Coupled Quark-Gluon Plasma, Prog. Part. Nucl. Phys. 62, 48 (2009), arXiv:0807.3033 [hep-ph]

    Article  ADS  Google Scholar 

  5. D. Kharzeev, E. Levin and K. Tuchin: QCD in Curved Space-Time: A Conformal Bag Model, Phys. Rev. D 70, 054005 (2004), arXiv:hep-ph/0403152

    ADS  Google Scholar 

  6. D. Kharzeev, E. Levin and K. Tuchin: Phys. Lett. B 547, 21 (2002), arXiv:hep-ph/0204274

    ADS  Google Scholar 

  7. D. Kharzeev, E. Levin and K. Tuchin: Broken Scale Invariance, Massless Dilaton and Confinement in QCD, arXiv:0809.3794 [hep-ph]

    Google Scholar 

  8. D. Kharzeev and K. Tuchin: From Color Glass Condensate to Quark Gluon Plasma Through the Event Horizon, Nucl. Phys. A 753, 316 (2005), arXiv:hepph/0501234

    ADS  Google Scholar 

  9. D. Kharzeev, E. Levin and K. Tuchin: Multi-Particle Production and Thermalization in High-Energy QCD, Phys. Rev. C 75, 044903 (2007), arXiv:hepph/0602063

    ADS  Google Scholar 

  10. P. Castorina, D. Kharzeev and H. Satz: Thermal Hadronization and Hawking-Unruh Radiation in QCD, Eur. Phys. J. C 52, 187 (2007), arXiv:0704.1426 [hep-ph]

    Article  ADS  Google Scholar 

  11. D. Kharzeev and K. Tuchin: Bulk Viscosity of QCD Matter Near the Critical Temperature, arXiv:0705.4280 [hep-ph]

    Google Scholar 

  12. F. Karsch, D. Kharzeev, K. Tuchin: Universal Properties of Bulk Viscosity Near the QCD Phase Transition, Phys. Lett. B 663, 217 (2008), arXiv:0711.0914 [hep-ph]

    ADS  Google Scholar 

  13. D.J. Gross and F. Wilczek: Ultraviolet Behavior of non-Abelian Gauge Theories, Phys. Rev. Lett. 30, 1343 (1973)

    Article  ADS  Google Scholar 

  14. H.D. Politzer: Reliable Perturbative Results for Strong Interactions?, Phys. Rev. Lett. 30, 1346 (1973)

    Article  ADS  Google Scholar 

  15. S. Bethke: Determination of the QCD Coupling αs, J. Phys. G 26, R27 (2000), arXiv:hep-ex/0004021

    ADS  Google Scholar 

  16. L.D. Landau and I.Y. Pomeranchuk: On Point Interactions in Quantum Electrodynamics, Dokl. Akad. Nauk Ser. Fiz. 102, 489 (1955); also published in Collected Papers of L.D. Landau, D. Ter Haar (ed.), pp. 654–658, Pergamon Press, Oxford (1965)

    Google Scholar 

  17. I.B. Khriplovich: Green’s Functions in Theories with non-Abelian Gauge Group, Yad. Fiz. 10, 409 (1969)

    Google Scholar 

  18. V.N. Gribov: Quantization of non-Abelian Gauge Theories, Nucl. Phys. B 139, 1 (1978)

    Article  MathSciNet  ADS  Google Scholar 

  19. D. Zwanziger: No Confinement Without Coulomb Confinement, Phys. Rev. Lett. 90, 102001 (2003), arXiv:hep-lat/0209105

    Article  ADS  Google Scholar 

  20. Y.L. Dokshitzer and D.E. Kharzeev: The Gribov Conception of Quantum Chromodynamics, Ann. Rev. Nucl. Part. Sci. 54, 487 (2004), arXiv:hep-ph/0404216

    Article  ADS  Google Scholar 

  21. J.R. Ellis: Aspects of Conformal Symmetry and Chirality, Nucl. Phys. B 22, 478 (1970)

    Article  ADS  Google Scholar 

  22. R.J. Crewther: Broken Scale Invariance in the Width of a Single Dilaton, Phys. Lett. B 33, 305 (1970)

    ADS  Google Scholar 

  23. M.S. Chanowitz and J.R. Ellis: Canonical Anomalies and Broken Scale Invariance, Phys. Lett. B 40, 397 (1972)

    ADS  Google Scholar 

  24. J. Schechter: Effective Lagrangian with Two Color Singlet Gluon Fields, Phys. Rev. D 21, 3393 (1980)

    ADS  Google Scholar 

  25. J.C. Collins, A. Duncan and S.D. Joglekar: Trace and Dilatation Anomalies in Gauge Theories, Phys. Rev. D 16, 438 (1977)

    ADS  Google Scholar 

  26. N.K. Nielsen: The Energy Momentum Tensor in a Nonabelian Quark Gluon Theory, Nucl. Phys. B 120, 212 (1977)

    Article  ADS  Google Scholar 

  27. M.A. Shifman, A.I. Vainshtein and V.I. Zakharov: QCD and Resonance Physics. Sum Rules, Nucl. Phys. B 147, 385 (1979)

    Article  ADS  Google Scholar 

  28. K. Wilson: Confinement of Quarks, Phys. Rev. D 10, 2445 (1974)

    ADS  Google Scholar 

  29. A. Ellis: Black Holes - History, Journal of the Astronomical Society of Edinburgh 39, (1999)

    Google Scholar 

  30. K. Schwarzschild: Ü ber das Gravitationsfeld eines Kugel aus inkompressibler Flüssigkeit nach der Einsteinschen Theorie, pp. 424–434, Sitzungsber. Preuss. Akad. D. Wiss. (1916)

    Google Scholar 

  31. J. Oppenheimer and G. Volkoff: On Massive Neutron Cores, Phys. Rev. 55, 374–381 (1939)

    Article  MATH  ADS  Google Scholar 

  32. D. Finkelstein: Past-Future Asymmetry of the Gravitational Field of a Point Particle, Phys. Rev. 110, 965–967 (1958)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  33. S. Hawking: Black Hole Explosions?, Nature 248, 3031 (1974)

    Article  Google Scholar 

  34. W. Busza, R. Jaffe, J. Sandweiss and F. Wilczek: Review of Speculative “Disaster Scenarios” at RHIC, arXiv:hep-ph/9910333

    Google Scholar 

  35. H. Nastase: The RHIC Fireball as a Dual Black Hole, arXiv:hep-th/0501068

    Google Scholar 

  36. R. Bousso: The Holographic Principle, arXiv:hep-th/0203101

    Google Scholar 

  37. H. Nastase: Introduction to AdS-CFT, arXiv:0712.0689 [hep-th]

    Google Scholar 

  38. O. Aharony, S. Gubser, J. Maldacena, H. Ooguri and Y. Oz: Large N Field Theories, String Theory and Gravity, Phys. Rept. 323, 183–386 (2000), arXiv:hepth/9905111

    Article  MathSciNet  ADS  Google Scholar 

  39. I. Klebanov: TASI Lectures – Introduction to the AdS/CFT Correspondence, arXiv:hep-th/0009139

    Google Scholar 

  40. V.A. Novikov, M.A. Shifman, A.I. Vainshtein and V.I. Zakharov: Are All Hadrons Alike?, Nucl. Phys. B 191, 301 (1981)

    Article  ADS  Google Scholar 

  41. A.A. Migdal and M.A. Shifman: Dilaton Effective Lagrangian in Gluodynamics, Phys. Lett. B 114, 445 (1982)

    ADS  Google Scholar 

  42. M. Novello, V.A. De Lorenci, J.M. Salimand R. Klippert: Geometrical Aspects of Light Propagation in Nonlinear Electrodynamics, Phys. Rev. D 61, 045001 (2000), arXiv:gr-qc/9911085

    ADS  Google Scholar 

  43. G. Policastro, D. Son and A. Starinets: Shear Viscosity of Strongly Coupled N = 4 Supersymmetric Yang-Mills Plasma, Phys. Rev. Lett. 87, 081601 (2001), arXiv:hep-th/0104066

    Article  ADS  Google Scholar 

  44. P. Arnold, C. Dogan and G. Moore: The Bulk Viscosity of High-Temperature QCD, Phys. Rev. D 74, 085021 (2006), arXiv:hep-ph/0608012

    ADS  Google Scholar 

  45. E. Lifshitz and L. Pitaevskii: Statistical Physics, Pt. 2, Sec. 90, Pergamon Press, New York (1980)

    Google Scholar 

  46. P. Kovtun, D. Son and A. Starinets: Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics, Phys. Rev. Lett. 94, 111601 (2005), arXiv:hep-th/0405231

    Article  ADS  Google Scholar 

  47. Y. Kats and P. Petrov: arXiv:0712.0743 [hep-th]

    Google Scholar 

  48. A. Buchel, R.C. Myers and A. Sinha: arXiv:0812.2521 [hep-th]

    Google Scholar 

  49. H. Meyer: A Calculation of the Shear Viscosity in SU(3) Gluodynamics, arXiv:0704.1801 [hep-lat]

    Google Scholar 

  50. A. Nakamura and S. Sakai: Transport Coefficients of Gluon Plasma, Phys. Rev. Lett. 94, 072305 (2005), arXiv:hep-lat/0406009

    Article  ADS  Google Scholar 

  51. K. Dusling and D. Teaney: Simulating Elliptic Flow with Viscous Hydrodynamics, Phys. Rev. C 77, 034905 (2008), arXiv:0710.5932 [nucl-th]

    ADS  Google Scholar 

  52. P. Romatschke and U. Romatschke: Viscosity Information from Relativistic Nuclear Collisions: How Perfect is the Fluid Observed at RHIC?, Phys. Rev. Lett. 99, 172301 (2007), arXiv:0706.1522 [nucl-th]

    Article  ADS  Google Scholar 

  53. M. Luzum and P. Romatschke: Conformal Relativistic Viscous Hydrodynamics: Applications to RHIC Results at 200 GeV, Phys. Rev. C 78, 034915 (2008), arXiv:0804.4015 [nucl-th]

    ADS  Google Scholar 

  54. H. Song and U.W. Heinz: Extracting the QGP Viscosity from RHIC Data – A Status Report from Viscous Hydrodynamics, arXiv:0812.4274 [nucl-th]

    Google Scholar 

  55. P. Ellis, J. Kapusta and H. Tang: Low-Energy Theorems for Gluodynamics at Finite Temperature, Phys. Lett. B 443, 63 (1998), arXiv:nucl-th/9807071

    ADS  Google Scholar 

  56. G. Boyd, J. Engels, K. Karsch, E. Laermann, C. Legeland, M. Luetgemeier and B. Petersson: Thermodynamics of SU(3) Lattice Gauge Theory, Nucl. Phys. B 469, 419–444 (1996), arXiv:hep-lat/9602007

    Article  ADS  Google Scholar 

  57. P. Benincasa, A. Buchel and A.O. Starinets: Sound Waves in Strongly Coupled non-Conformal Gauge Theory Plasma, Nucl. Phys. B 733, 160 (2005), arXiv:hepth/0507026

    MathSciNet  ADS  Google Scholar 

  58. H. Meyer: A Calculation of the Bulk Viscosity in SU(3) Gluodynamics, arXiv:0710.3717 [hep-lat]

    Google Scholar 

  59. A. Nakamura and S. Sakai: Lattice Calculation of the QGP Viscosities, arXiv:0710.3625 [hep-lat]

    Google Scholar 

  60. A. Kogan and H. Meyer: J. Low Temp. Phys. 110, 899 (1998)

    Article  Google Scholar 

  61. M. Cheng et al: The QCD Equation of State with Almost Physical Quark Masses, arXiv:0710.0354 [hep-lat]

    Google Scholar 

  62. K. Paech and S. Pratt: Origins of Bulk Viscosity at RHIC, Phys. Rev. C 74, 014901 (2006), arXiv:nucl-th/0604008

    ADS  Google Scholar 

  63. J.W. Chen and J. Wang: Bulk Viscosity of a Gas of Massless Pions, arXiv:0711.4824 [hep-ph]

    Google Scholar 

  64. D. Fernandez-Fraile and A.G. Nicola: Bulk Viscosity and the Conformal Anomaly in the Pion Gas, arXiv:0809.4663 [hep-ph]

    Google Scholar 

  65. J. Noronha-Hostler, J. Noronha and C. Greiner: Transport Coefficients of Hadronic Matter Near T c , arXiv:0811.1571 [nucl-th]

    Google Scholar 

  66. C. Sasaki and K. Redlich: Transport Coefficients Near Chiral Phase Transition, arXiv:0811.4708 [hep-ph]

    Google Scholar 

  67. S. Gubser, A. Nellore, S. Pufu and F. Rocha: Thermodynamics and Bulk Viscosity of Approximate Black Hole Duals to Finite Temperature Quantum Chromodynamics, arXiv:0804.1950 [hep-th]

    Google Scholar 

  68. S. Gubser, S. Pufu and F. Rocha: Bulk Viscosity of Strongly Coupled Plasmas with Holographic Duals, arXiv:0806.0407 [hep-th]

    Google Scholar 

  69. G. Torrieri and I. Mishustin, Instability of Boost-Invariant Hydrodynamics with a QCD Inspired Bulk Viscosity, Phys. Rev. C 78, 021901 (2008), arXiv:0805.0442 [hep-ph]

    ADS  Google Scholar 

  70. A. Karch, E. Katz, D.T. Son and M.A. Stephanov, Linear Confinement and AdS/QCD, Phys. Rev. D 74, 015005 (2006), arXiv:hep-ph/0602229

    ADS  Google Scholar 

  71. U. Gursoy and E. Kiritsis, Exploring Improved Holographic Theories for QCD, JHEP 0802, 032 (2008), arXiv:0707.1324 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  72. U. Gursoy and E. Kiritsis: Exploring Improved Holographic Theories for QCD, JHEP 0802, 019 (2008), arXiv:0707.1349 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

Download references

Acknowledgments

D.K. is grateful to H. Satz and B. Sinha for the invitation to deliver these lectures and the hospitality in Jaipur. The work of D.K. was supported by the U.S. Department of Energy under Contract No. DE-AC02-98CH10886

Author information

Authors and Affiliations

  1. Department of Physics, Princeton University, 08544, Princeton, NJ, USA

    Theodor Bra³oveanu

  2. Department of Physics, Brookhaven National Laboratory, 11973-5000, Upton, NY, USA

    Dmitri Kharzeev

  3. Helmholtz Research School and Otto Stern School, Goethe-Universität Frankfurt am Main, Frankfurt, Germany

    Mauricio Martinez

Authors
  1. Theodor Bra³oveanu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dmitri Kharzeev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mauricio Martinez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Theodor Bra³oveanu .

Editor information

Editors and Affiliations

  1. Centre (VECC), Variable Energy Cyclotron, Bidhan Nagar, Kolkata, 700064, India

    Sourav Sarkar

  2. Fak. Physik, Universität Bielefeld, Universitätsstr. 25, Bielefeld, 33615, Germany

    Helmut Satz

  3. Centre (VECC), Variable Energy Cyclotron, Bidhan Nagar, Kolkata, 700064, India

    Bikash Sinha

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Bra³oveanu, T., Kharzeev, D., Martinez, M. (2009). In Search of the QCD–Gravity Correspondence. In: Sarkar, S., Satz, H., Sinha, B. (eds) The Physics of the Quark-Gluon Plasma. Lecture Notes in Physics, vol 785. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02286-9_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02286-9_10

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02285-2

  • Online ISBN: 978-3-642-02286-9

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics

Search

Navigation