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On viscosity of Quark Gluon Plasma

On viscosity of Quark Gluon Plasma. Defu Hou CCNU , Wuhan . RHIC-Star full TOF detector and related physics in China Hangzhou April 27-29. Outlines. Introduction and motivation Viscosity from Kubo formula Viscosity from kinetic theory (Boltzmann Eq) Viscosity from AdS/CFT

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On viscosity of Quark Gluon Plasma

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  1. On viscosity of Quark Gluon Plasma Defu Hou CCNU , Wuhan RHIC-Star full TOF detector and related physics in China Hangzhou April 27-29

  2. Outlines • Introduction and motivation • Viscosity from Kubo formula • Viscosity from kinetic theory (Boltzmann Eq) • Viscosity from AdS/CFT • Summary

  3. QCD under extreme conditions • At very High T or density ( deconfined) • High T (Early universe, heavy-ion collisions) • High density matter ( in the core of neutron stars)

  4. Motivations Experiments aspect: @ RHIC • Robust collective flows, well described by ideal hydro with Lattice-based EoS. This indicates very strong interaction even at early time => sQGP • sQGP seems to be the almost perfect fluid known /s>= .1-.2<<1

  5. Study of dissipative effects on <v2> How sensitive is elliptic flow to finite /s? Viscous Hydro Cascade (2<->2,2<->3) P. Romatschke, PRL99 (07) Z. Xu & C. Greiner, PRL 101(08) Agreement for s=0.3 – 0.6 Dependence on tp relaxation time II0 order expansion with green terms (D. Rischke) /s=0.15 – 0.08

  6. Theoretic aspect: • To calculate Trsp. Coefs. in FT in highly nontrivial (nonperturbative ladder resummation) (c around 5) • String theory method: AdS/CFT (D.Son et al 2003) /s = 1/4 . Kinetic theory + uncertainty principle (Gyulassy)

  7. Main obstacle for theory • QCD in nonperturbative regime (T~200Mev) • Pertburb. Expansion of QCD is not well behaved for realistic T • For thermodyn.,one can use lattice and resummation techniques • Kinetic coefficients are difficult to extract from lattice

  8. Shear Viscosity

  9. Viscosity from Kubo formula

  10. Nonlinear Response

  11. S. Jeon, PRD 52; Carrington, Hou, Kobes, PRD61

  12. Carrington, Hou, Kobes, PRD64 (2001)

  13. Hou, hep-ph/0501284

  14. Viscosity from kinetics theory

  15. Fluctuation of distribution (s: species) Viscosity of hot QCD at finite density Boltzmann Equation Recast the Boltzmann equation P.Arnold, G.D.Moore and G.Yaffe, JHEP 0011(00)001

  16. Shear viscosity With a definition of inner product and expanded distribution functions, where

  17. Performing the integral over dk’ with the help of Collision terms \chi term Scattering amplitude Distribution function term

  18. Matrix Element

  19. Variation method gives Liu, Hou, Li EPJC 45(2006)

  20. Computing transport coefficients from AdS/CFT In the regime described by a gravity dual the correlator can be computed using AdS/CFT

  21. = conjecture AdS/CFT at finite temperature Classical Supergravity on AdS-BH×S5 Witten ‘98 4dim. Large-Nc strongly coupled SU(Nc) N=4 SYM at finite temperature (in the deconfinement phase).

  22. = Field TheoryGravity Theory Gauge Theories QCD Quantum Gravity String theory Holography the large N limit Supersymmetric Yang Mills N large Gravitational theory in 10 dimensions Calculations Correlation functions Quark-antiquark potential

  23. AdS/CFT now being applied to RHIC physics • Viscosity, /s. • EOS • Jet quenching • “Sound” waves • Photon production • Friction … • Heavy quarkonium • Hardron spectrum (ADS/QCD)

  24. Universality of shear viscosity in the regime described by gravity duals Graviton’s component obeys equation for a minimally coupled massless scalar. But then . Since theentropy (density) is we get D. Son, P. Kovtun, A.S., hep-th/0405231

  25. Shear viscosity in SYM P.Arnold, G.Moore, L.Yaffe, 2001 Correction to : A.Buchel, J.Liu, A.S., hep-th/0406264

  26. A viscosity bound conjecture P.Kovtun, D.Son, A.S., hep-th/0309213, hep-th/0405231

  27. Universality of Theorem: For any thermal gauge theory (with zero chemical potential), the ratio of shear viscosity to entropy density is equal to in the regime described by a corresponding dual gravity theory Remark: Gravity dual to QCD (if it exists at all) is currently unknown.

  28. Possible Mechanisms for Low viscosity • Large cross-section, strong coupling • Anomalous viscosity: turbulence M. Asakawa, S.A. Bass, B.M., hep-ph/0603092, PRL See Abe & Niu (1980) for effect in EM plasmas

  29. M. Asakawa, S.A. Bass, B.M., hep-ph/0603092 See Abe & Niu (1980) for effect in EM plasmas Take moments of with pz2

  30. Low viscosity due to Anderson Local. • AL effect renders infinite reduces viscosity significantly even at weak coupling • Mechanism:coherent backscattering (CBS) effect Ginaaki, Hou , Ren PRD 77(2008)

  31. Summary • Kubo formula: via correlation functions of currents • Transport theory: Boltzmann Eqs. (for weak scattering) • ADS/CFT(strongly coupled) • Lattice calculation (noisy) Approches to calculate viscosity

  32. Thanks

  33. Renormalized diffusion

  34. Weak Localization (WL) • Anderson proposed (‘58) that electronic diffusion can vanish in a random potential (AL) • Experiments detected ( Ishimaru 1984,Wolf Maret 1985) • Mechanism:coherent backscattering (CBS) effect after a wave is multiply scattered many times， its phase coherence is preserved in the backscattering direction， the probability of back scattering is enhenced via constructive interference

  35. Viscosity with random medium System: quasi-particles in random potential • Candidate disorder in sQGP ? • The islands of heavy state; bound states (Shuryak); • 2. The reminiscent of confinement vaccum, say the domain structure of 't Hooft's monopole condensation; • The disoriented chiral condensate (DCC); • 4. CGC

  36. Response function

  37. BS Eq. In Diagrams

  38. Localization length • Itinerant states ---- Localized States

  39. II Some applications to N=4 SUSY YM Plasma: Equation of state in strong coupling: Plasma temperature = Hawking temperature Near Schwarzschild horizon Continuating to Euclidean time, To avoid a conic singularity at , the period of Recalling the Matsubara formulation

  40. Free energy = temperature X (the gravity action without metric fluctuations)E. Witten, Adv. Theor. Math. Phys. 2, 505 (1998), hep-th/9803131. Consider a 4D Euclidean space of spatial volume V_3 at The EH action of AdS-Schwarzschild: The EH action of plain AdS ----- To eliminate the conic singularity, ----- To match the proper length in Euclidean time Plasma free energy: Plasma entropy:

  41. Bekenstein-Hawking entropy: Gubser, Klebanov & Pest, PRD54, 3915 (1996) ------ The metric on the horizon： ------ The gravitational constant of the dual: agree with the entropy extraced from the gravity action.

  42. The ratio 3/4: The plasma entropy density at The free field limit: The lattice QCD yields

  43. Shear viscosity in strong coupling: Policastro, Son and Starinets, JHEP09, 043 (2002) Kubo formula where

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