Holographic description of heavy-ions collisions

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Holographic description of heavy-ions collisions

• Irina Arefeva
• Steklov Mathematical Institute, Moscow

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

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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

170 MeV
300 MeV
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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
  pp)
• jet quenching
• high p_T-suppression of hadrons
• elliptic flow
• suppression of quarkonium production

Study of this medium is also related with study
of Early Universe
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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 a Heavy Ion Collision
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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 ? for gravity.
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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
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
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pp collisions vs heavy ions collisions
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QGP in heavy-ions collisions
There are strong experimental evidences that
RHIC or LHC have created some medium
Elliptic flow
more pressure along the small axis
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Multiplicity Landaus/Hologhrapic formula
vs experimental data
Landau formula
Plot from ATLAS Collaboration 1108.6027
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Multiplicity
s1/2NN dependence of the charged particle dNch/
dh h 0 per colliding nucleon pair Npart/2
from a variety of measurements in pp and p-p
and central AA collisions, 0-5 centrality
ALICE and CMS The curves show different
expectations for the s1/2NN dependence in AA
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)
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Multiplicity in Landau model
BACKUP
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
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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

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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

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Holography and duality.
Holography t Hooft, 1993 Susskind, 1994
D4 D3
D4
D4 Gauge theory N4 YM with SU(Nc)
Duality
Group symmetry
bosonic part SO(2,4) x SU(4) lt-gt
isometries of AdS5xS5 conformal symmetry and
R-symmetry
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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 gt300
  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
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AdS/CFT correspondence in Euclidean space. T0
The correspondence between the strongly coupled N
4 SYM theory in D4 and classical
(super)gravity on AdS5xS5
WittenGubser, Klebanov, Polyakov,1998
IA, I.Volovich, PLB, 1998
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AdS/CFT correspondence in Minkowski space.
incoming wave at
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AdS/CFT correspondence in Euclidean space. T0
denotes Euclidean time ordering
requirement of regularity at horizon
g
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AdS/CFT correspondence. Minkowski. T0
QFT at finite temperature (D4)
Classical gravity with black hole (D5)
LHS
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AdS/CFT correspondence. T0
Gravity AdS5 with black hole
RHS
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Dual description of QGP as a part of
gauge/string duality
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.
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Dual description of QGP as a part of
gauge/string duality
Janik, 05
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Conclusion
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

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D2 CFT at T0 and BTZ black hole
Backup
2D CFT
Conformal map from the infinite plane to the
cylinder with circumference L1/T
()
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D2 CFT at T0 and BTZ black hole
Backup
Gravity calculations
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Backup
D2 CFT at T0 and BTZ black hole
()
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D2 CFT at T0 and BTZ black hole
Backup
tIdentification of the prefactors
Retarded Greens () taken at
are equal to the expression given by eq. ()
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Relation between Bogoliubov-Tyablikov GR and
Matsubara GE Green functions
BACKUP
Bogoliubov-Tyablikov
Matsubara
denotes Euclidean time ordering