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),