Holographic description of heavy-ions collisions Irina Aref’eva Steklov Mathematical Institute, Moscow 7th MATHEMATICAL PHYSICS MEETING: Summer School and Conference on Modern Mathematical Physics 9 - 19 September 2012, Belgrade, Serbia

Outlook Physical picture of formation of Quark-Gluon Plasma in heavy-ions collisions Holography description of QGP in equilibrium Holography description of heavy-ions collisions New formula for multiplicity Further directions

Quark-Gluon Plasma (QGP): a new state of matter QGP is a state of matter formed from deconfined quarks, antiquarks, and gluons at high temperature QCD: asymptotic freedom, quark confinement nuclear matter Deconfined phase T increases, or density increases Нагревать= warm up, 150MeV= K ЧИСЛА! Mu_b baryon chemical potential 170 MeV 300 MeV

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. Text from 1102.3010v2.pdf 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 hadrons elliptic flow suppression of quarkonium production 4 Study of this medium is also related with study of Early Universe

QGP in Heavy Ion Collision and Early Universe One 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 the Early Universe 170 MeV 1K=10 ^{-13}GeV Evolution of a Heavy Ion Collision

The Standard Model of Nature 1. A Gauge Theory with a light Higgs for electro-weak and strong interactions. 2. General Relativity with a small Λ for gravity.

Theory. Heavy Ions collisions Macroscopic: thermodynamics, hydrodynamics, kinetic theory, … Fermi(1950); Pomeranchuk(1952); Landau(1953); Heisenberg(1952), Rozental, Chernavskij (UFN,1954); Landau, Bilenkij (UFN,1955); Feinberg (1972); Cooper,…(1975); Bjorken(1983); 1950-th the hydrodynamic model to high energy collisions of protons Text from 1102.3010v2.pdf 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 7

pp collisions vs heavy ions collisions Pb Pb PbPb – lead-lead

QGP in heavy-ions collisions There are strong experimental evidences that RHIC or LHC have created some medium: Elliptic flow Text and picture from Son-cern2008 more pressure along the small axis 9

Multiplicity: Landau’s/Hologhrapic formula vs experimental data Landau formula Plot from: Alice Collaboration PRL, 2010 dNch/dη ≈ 1600 ± 76 (syst) ≈ 30,000 particles in total, ≈ 400 times pp ! Energy density ε > 3 x RHIC (fixed τ0,) Temperature + 30% Plot from: ATLAS Collaboration 1108.6027 Simplest Hologhrapic Model Modified Hologhrapic Model

Multiplicity 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 in Landau model BACKUP Multiplicity in Landau model Thermodynamic 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 collision 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-pdV Dividing on dV we get eq. for densities s=dS/dV, etc. V~m0/E means the Lorentz contraction

QGP as a strongly coupled fluid Conclusion 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. Holography: ‘t Hooft, 1993; Susskind, 1994 Strings Maldacena 1997: D=4 Gauge Theory D=5 D=4 D=3 D=4 ‘t Hooft, “dimensional reduction in quantum gravity” gr-qc/9310026 Susskind, “The World as a hologram” hep-th/9409089 String theory on AdS5xS5 Gravity in AdS5 Duality: D=4 Gauge theory N=4 YM with SU(Nc) Group symmetry bosonic part SO(2,4) x SU(4) <-> isometries of AdS5xS5 conformal symmetry and R-symmetry

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=0 The correspondence between the strongly coupled N = 4 SYM theory in D=4 and classical (super)gravity on AdS5xS5 Simplest case: Witten;Gubser, Klebanov, Polyakov,1998 Renormalization IA, I.Volovich, PLB, 1998

AdS/CFT correspondence in Minkowski space. incoming wave at

AdS/CFT correspondence in Euclidean space. T=0 denotes Euclidean time ordering + requirement of regularity at horizon 19

AdS/CFT correspondence. T=0 QFT at finite temperature (D=4) Classical gravity with black hole (D=5) -- retarded temperature Green function in 4-dim Minkowski F -- kernel of the action for the (scalar) field in AdS5 Son, Starinets, 2002 QFT with T Bogoliubov-Tyablikov Green function

AdS/CFT correspondence. T=0 Gravity: AdS5 with black hole fk(z) is the solution to the mode equation: with unit boundary conditions:

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

D=2 CFT at T=0 and BTZ black hole Euclidean finite temperature correlates of the local operator with conformal dimension Conformal map from the infinite plane to the cylinder with circumference L=1/T (*)

D=2 CFT at T=0 and BTZ black hole Gravity calculations

D=2 CFT at T=0 and BTZ black hole On shell Boundaries: (**)

D=2 CFT at T=0 and BTZ black hole tIdentification of the prefactors Retarded Green’s (**) taken at are equal to the expression given by eq. (*)

BACKUP Relation between Bogoliubov-Tyablikov GR and Matsubara GE Green functions Bogoliubov-Tyablikov Matsubara denotes Euclidean time ordering

Dual description of QGP as a part of gauge/string duality In the phenomenological hydrodynamical (Landau or Bjorken models of QGP), the plasma is characterized by a space-time profile of the energy-momentum tensor AdS/CFT: operators in the gauge theory correspond to fields in SUGRA . In the case of the energy-momentum tensor, the corresponding field is the 5D metric.

Dual description of QGP as a part of gauge/string duality Static uniform plasma Janik, 05 REF.-exact Solution: Performing a change of coordinates The standard AdS static black hole

Conclusion Black Hole in AdS5  static QGP in 4-dim Today: 2001-2011 Black Hole in AdS5  static QGP in 4-dim Formula for correlates Static uniform plasma  BH AdS Tomorrow: 2008-now formation of QGP  formation of BH in AdS