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  • Holographic description of heavy-ions collisions

    Irina Arefeva

    Steklov Mathematical Institute, Moscow

    7th MATHEMATICAL PHYSICS MEETING: Summer School and Conference on Modern Mathematical Physics 9 - 19 September 2012, Belgrade, Serbia

  • OutlookPhysical picture of formation of Quark-Gluon Plasma in heavy-ions collisionsHolography description of QGP in equilibrium Holography description of heavy-ions collisionsNew formula for multiplicityFurther directions

  • Quark-Gluon Plasma (QGP): a new state of matterQGP is a state of matter formed from deconfined quarks, antiquarks, and gluons at high temperature300 MeV170 MeV

    QCD: asymptotic freedom, quark confinement

  • Experiments: Heavy Ions collisions produced a medium HIC are studied in several experiments: started in the 1990's at the Brookhaven Alternating Gradient Synchrotron (AGS), the CERN Super Proton Synchrotron (SPS) the Brookhaven Relativistic Heavy-Ion Collider (RHIC) the LHC collider at CERN.

    There are strong experimental evidences that RHIC or LHC have created some medium which behaves collectively:

    modification of particle spectra (compared to p+p)jet quenching high p_T-suppression of hadronselliptic flowsuppression of quarkonium production Study of this medium is also related with study of Early Universe

  • QGP in Heavy Ion Collision and Early UniverseOne of the fundamental questions in physics is: what happens to matter at extreme densities and temperatures as may have existed in the first microseconds after the Big Bang The aim of heavy-ion physics is to create such a state of matter in the laboratory.

    Evolution of a Heavy Ion Collision

  • The Standard Model of Nature1. A Gauge Theory with a light Higgs for electro-weak and strong interactions.2. General Relativity with a small for gravity.

  • Theory. Heavy Ions collisionsMacroscopic: thermodynamics, hydrodynamics, kinetic theory,

    1950-th the hydrodynamic model to high energy collisions of protons Fermi(1950); Pomeranchuk(1952); Landau(1953); Heisenberg(1952), Rozental, Chernavskij (UFN,1954); Landau, Bilenkij (UFN,1955); Feinberg (1972); Cooper,(1975); Bjorken(1983);

    Kolb, Heinz (2003); Janik, Peschansky (2006); Shuryak(,,,,, 2009); Peigne, Smilga (UFN, 2009)Dremin, Leonidov (UFN, 2010); Muller, Schafer(2011),. Microscopic: - QCD, holographic (AdS/CFT)Application of holographic approach to formation of QGP is the subject of this talk

  • pp collisions vs heavy ions collisions

  • There are strong experimental evidences that RHIC or LHC have created some medium: QGP in heavy-ions collisions Elliptic flow

    more pressure along the small axis

  • Multiplicity: Landaus/Hologhrapic formula vs experimental dataLandau formulaPlot from: ATLAS Collaboration 1108.6027

  • s1/2NN dependence of the charged particle dNch/ dh | h =0 per colliding nucleon pair Npart/2 from a variety of measurements in p+p and p+-p and central A+A collisions, 0-5% centrality ALICE and CMS

    The curves show different expectations for the s1/2NN dependence in A+A collisions: results of a Landau hydrodynamics calculation (dotted line) ; an s0.15 extrapolation of RHIC and SPS data (dashed line); a logarithmic extrapolation of RHIC and SPS data (solid line)Multiplicity

  • Multiplicity in Landau modelThermodynamic methods to investigating the process of high-energy collision.E. Fermi, Prog. Theor. Phys. 5, 570 (1950)Pomeranchuk, Dokl. Akad. Nauk SSSR, 78, 889 (1951)L. D. Landau, Izv. Akad. Nauk Ser. Fiz. 17, 51 (1953)To determine the total number of particles it is necessary to compute the entropy in the first moment of collisionBACKUP

  • QGP as a strongly coupled fluidConclusion from the RHIC and LHC experiments: appearance of QGP (not a weakly coupled gas of quarks and gluons, but a strongly coupled fluid).

    This makes perturbative methods inapplicable

    The lattice formulation of QCD does not work, since we have to study real-time phenomena.

    This has provided a motivation to try to understand the dynamics of QGP through the gauge/string duality

  • Holographic description of quark-gluon plasma

    Holographic description of quark-gluon plasma in equilibrium Holography description of quark-gluon plasma formation in heavy-ions collisions

  • Holography and duality.Duality:D=4 Gauge theoryN=4 YM with SU(Nc)Holography: t Hooft, 1993; Susskind, 1994D=4Group symmetrybosonic part SO(2,4) x SU(4) isometries of AdS5xS5 conformal symmetry and R-symmetryD=4

    D=3

  • Dual description of QGP as a part of Gauge/string duality There is not yet exist a gravity dual construction for QCD. Differences between N = 4 SYM and QCD are less significant, when quarks and gluons are in the deconfined phase (because of the conformal symmetry at the quantum level N = 4 SYM theory does not exhibit confinement.)

    Lattice calculations show that QCD exhibits a quasi-conformal behavior at temperatures T >300 MeV and the equation of state can be approximated by e = 3 p (a traceless conformal energy-momentum tensor).

    The above observations, have motivated to use the AdS/CFT correspondence as a tool to get non-perturbative dynamics of QGP.

    There is the considerable success in description of the static QGP.Review: Solana, Liu, Mateos, Rajagopal, Wiedemann, 1101.0618

  • AdS/CFT correspondence in Euclidean space. T=0The correspondence between the strongly coupled N = 4 SYM theory in D=4 and classical (super)gravity on AdS5xS5Witten;Gubser, Klebanov,Polyakov,1998IA, I.Volovich, PLB, 1998

  • AdS/CFT correspondence in Minkowski space. incoming wave at

  • AdS/CFT correspondence in Euclidean space. T=0denotes Euclidean time ordering+ requirement of regularity at horizong:

  • AdS/CFT correspondence. Minkowski. T=0QFT at finite temperature (D=4)Classical gravity with black hole (D=5)LHS

  • AdS/CFT correspondence. T=0Gravity: AdS5 with black holeRHS

  • Dual description of QGP as a part of gauge/string duality. In the case of the energy-momentum tensor, the corresponding field is the 5D metric.AdS/CFT: operators in the gauge theory correspond to fields in SUGRA

  • Janik, 05Dual description of QGP as a part of gauge/string duality

  • ConclusionBlack Hole in AdS5 static QGP in 4-dim Formula for correlates Static uniform plasma BH AdS

    2001-2011 formation of QGP formation of BH in AdS

    Today:Tomorrow:2008-now

  • D=2 CFT at T=0 and BTZ black hole2D CFTConformal map from the infinite plane to the cylinder with circumference L=1/T(*)Backup

  • D=2 CFT at T=0 and BTZ black holeGravity calculationsBackup

  • D=2 CFT at T=0 and BTZ black hole(**)Backup

  • D=2 CFT at T=0 and BTZ black holetIdentification of the prefactorsRetarded Greens (**) taken at are equal to the expression given by eq. (*) Backup

  • Relation between Bogoliubov-Tyablikov GR and Matsubara GE Green functionsdenotes Euclidean time orderingMatsubaraBogoliubov-TyablikovBACKUP

    *= warm up,150MeV= K!

    Mu_b baryon chemical potential*Text from 1102.3010v2.pdf*170 MeV1K=10 ^{-13}GeV*Text from 1102.3010v2.pdf*PbPb lead-lead*Text and picture from Son-cern2008*dNch/d 1600 76 (syst) 30,000 particles in total, 400 times pp !

    Energy density > 3 x RHIC (fixed 0,)

    Temperature + 30%

    *Key[i:] ideal: E. Fermi, Prog. Theor. Phys. 5, 570 (1950)L. D. Landau, Izv. Akad. Nauk Ser. Fiz. 17, 51 (1953)R. Hagedorn, CERN-Report 71-12 (1971).

    Main eq. is dE=TdS-pdVDividing on dV we get eq. for densitiess=dS/dV, etc.V~m0/E means the Lorentz contraction*t Hooft, dimensional reduction in quantum gravity gr-qc/9310026Susskind, The World as a hologram hep-th/9409089

    *****REF.-exact*

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