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Holographic Description of Quark-Gluon Plasma
Irina Aref'eva Steklov Mathematical Institute, RAN, Moscow
JINR, Dubna
March 19, 2014
Quark-Gluon Plasma Formation in Heavy Ion Collisions
in Holographic Description
JINR, Dubna
April 3, 2013
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
nuclear matter
Deconfined phase
T increases, or density increases
QCD: asymptotic freedom, quark confinement
Outlook (Last year)
• Quark-Gluon Plasma(QGP) in heavy-ions collisions(HIC)• Holography description of QGP in equilibrium • Holography description of formation of QGP in HIC <=> Black Holes formation in AdS• Thermalization time/Dethermalization time• Non-central collisions in holography description
QGP in Heavy Ion Collision
• 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
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
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 = 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, 1101.0618I.A. UFN, 2014
What we know
• Multiplicity
• Thermalization time• Interquark potential
• Hard probes (transport coefficients drag force, jet quenching,…)
Multiplicity
Plot from: ATLAS Collaboration 1108.6027
0.25NNs
0.15NNs
0.11NNs
“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
AdS/CFT correspondence
+ requirement of regularity at horizon
0|( , , ), [ ], [ ] | 0c Mg g cx z S S
0
Me
O
0[ ( )]g cSe
Gubser,Klebanov,Polyakov Witten, 1998
M=AdS
AdS/CFT Correspondence via Geodesics.
Example I. D=2
x-x’=
AdS3
x x’
2
2222
z
dzdxdtds
2
1( , ) ( , ') ~
| ' |O t x O t x
x x
Correlators with T=0
z0
Correlators with T via AdS/CFT
Example II. D=2
BHAdS
Bose gas
Temperatute
2
1( , ) ( , ') ~
| sinh( | ' |) |TO t x O t xT x x
T2
Average of non-local operator with a contour on the boundary = action of a classical string ending on the contour
AdS/CFT correspondence for non-local operator :
))(exp()( 1. ritVCW rect
)(1 rV is the singlet potential of interquark interaction
Maldacena hep-th/9803002
)exp(1
)( Cc
AgTrPN
CW
SeCW )(
5AdS
)(1
ds 2222
2 xddzdtz
r
CrV )(
)(LCP
5)( AdSEBHP
))(
)((1
ds 22
22
2 xdzf
dzdtzf
z
4Mz-1f(z)
)(1
-)(V 4BrAr
r
Sonneschein…hep-th/9803137; Rey, Yee…hep-th/9803135
)),(exp(
1)(
0
4
drAgPTrN
rLc
)(1)()0( rVerLL
BTZ –metric
22
222
2
42
22 1
21
1)
1(ds d
zadtd
zaz
M
dz
zdt
zM
22
222
2
42
22 1
21
1)
1(ds d
zadtd
zaz
M
dz
zdt
zM
LorentzLorentz
EuclideanEuclidean
(Banados,Teitelboim,Zanelli; 1992)(Banados,Teitelboim,Zanelli; 1992)
20 t0z
t0
Classical string actions and parametrization
)(),( zX
t
)det(2
2
hdTS
1
1
Lorentz
Euclidean
Potential:
MV )(1
For some phi there is a string breaking!
Holography for thermal states
TQFT in
MD-spacetime
Black holein AdSD+1-space-time =
Hologhraphic description of QGP
(QGP in equilibruum)
TQFT = QFT with temperature
Hologhraphic thermalization
Thermalization of QFT in Minkowski D-dim space-
time
Black Hole formation in Anti de Sitter (D+1)-dim space-time
Hologhraphic Description of Formation of QGP
Studies of BH formation in AdSD+1
Time of thermalization in HIC
Multiplicity in HIC
Profit:
• colliding gravitational shock waves
• drop of a shell of matter
("null dust"), infalling shell geometry = Vaidya metric
• sudden perturbations of the metric near the boundary that propagate into the bulk
Formation of BH in AdS. Deformations of AdS metric leading to BH formation
Gubser, Pufu, Yarom, Phys.Rev. , 2008 JHEP , 2009 Alvarez-Gaume, C. Gomez, Vera, Tavanfar, Vazquez-Mozo, PRL, 2009IA, Bagrov, Guseva, Joukowskaya, E.Pozdeeva, 2009, 2010, 2012 JHEPKiritsis, Taliotis, 2011 JHEP
Danielsson, Keski-Vakkuri , Kruczenski, 1999 ……Balasubramanian +9. PRL, 2011,Phys.Rev.2011,…..IA,IVolovich, 2013; IA,Bagrov,Koshelev,2013
Chesler, Yaffe, PRL, 2011
Colliding gravitational shock waves
)5()5()5(MNMNMN ggg
• AdS/CFT correspondence
)4(
0
)5( |)( TgzZzboundaryren
Nucleus collision in AdS/CFT
)(~ xT
The metric of two shock waves in AdS corresponding to collision of two ultrarelativistic nucleus in 4D
2 2 22 4 2 4 2 2 2
2 2 2
2 22 ( ) ( )
C C
Lds dx dx T x z dx T x z dx dx dz
z N N
x
x
~ ( )T x
Multiplicity: Hologhrapic formula vs experimental data
Plot from: ATLAS Collaboration 1108.6027
0.25NNs
0.15NNs
0.11NNs
The mininal black hole entropy can be estimated by trapped surface area
We describe heavy-ion collisions by the wall-wall shockwave collisions in (or in its modification) S. Lin, E. Shuryak, 1011.1918 I. A., A. A. Bagrov and E. O. Pozdeeva,(2012)
We describe heavy-ion collisions by the wall-wall shockwave collisions in (or in its modification) S. Lin, E. Shuryak, 1011.1918 I. A., Bagrov and E.Pozdeeva,(2012)
Shock wave metric modified by b-factor
The Einstein equation for particle in dilaton field
Shock wave metric modified by b-factor
The Einstein equation for particle in dilaton field
I. A., E.Pozdeeva,T.Pozdeeva (2013,2014)
AdS space-time modifications
For the standard AdS space-time b(z) factor has form b(z)=L/z
b-factors in modify AdS space-time
Mixed factor
a=1/2
Backup
Power-law wrapping factor
S=
The multiplicity of particles produced in HIC(PbPb-and AuAu-collisions) dependents
as s0.15NN in the range 10-103 GeV
Power-law b-factor coinsides with experimental data at a≈0.47
Dilaton potential
Thermalization Time
Thermalization Time (via Vaidya) and Centricity
Non-centricity Kerr-ADS-BH
I.A. A.Koshelev, A.Bagrov, JHEP, 013
)0()0( aa
D=3
D>3, in progress
ConclusionFormation of QGP of 4-dim QCD Black Hole formation in AdS5
• Multiplicity: AdS-estimations fit experimental data
• Non-centricity decreases thermalization time.
0.15data NNS s
• Drag forces (in progress),