Heavy-quark potential from AdS/CFT

侯 德 富

华中师范大学粒子物理研究所

两岸粒子物理与宇宙学研讨会， 重庆， 2012 年 5 月

• Introduction

• Holographic potential and melting T

• Subleading order potential from AdS/CFT

• Summary

OUTLINES

Zhang, Hou, Ren,Yin JHEP07:035 （ 2011 ）

Hou, Liu, Li, Ren, JHEP 1007:042 (2010)Hou, Ren JHEP01:029 （ 2008 ） Chu, Hou , Ren JHEP08: 004 (2009)

Hou, Liu, Ren, PRD80:046007 (2009)

QCD Phase Structure

Many interesting phenomena in QCD lie in the strongly-coupled region

Type II B Super String theory on AdS-BH×S5

4dim. Large-Nc strongly coupledSU(Nc) N=4 SYM ( finite T).

conjecture

=

Witten ‘98 Maldacena ‘97

AdS/CFT corerspondence

(x)])0,([

4

)2

1 tension(string

1

bulk in the theory string IIB Type boundary on the YM SUSY 4

0string

)()(

22

04

xZe

gN

gN

N

xOxxd

sc

YMc

actionty supergravi classical][

|)]()0,([

and limit In the

sugra

)()0,(][

0string 0

sugra

I

exxZ

N

xxI

c

‘t Hooft coupling

AdS/CFT applied to RHIC physics

• Viscosity, /s.

• Thermodynamics.

• Jet quenching

• Photon production, Friction

• Heavy quarkonium (hard probe)• Hardron spectrum (ADS/QCD) wu, Huang et al

• …..

)0(

4

3ss

Liu, Rajagopal and Wiederman

4

1

s Policastro, Son and Starinet

Witten

32

3

4

54

3

ˆ Tq

Heavy quark potential probes confinement hadronic phase and meson melting in plasma

• Shear viscosity: Policastro, Son and Starinets

---- Kubo formula

---- AdS/CFT recipe: The coefficient of the

y

x

y

vf x

The friction force per unit area

2xyh term of the gravity action

)0(),()(),(

)0,(Im1

lim

,

,0

xyxyxitiR

xyxy

Rxyxy

TxTtedtdG

G

qxqwhere

dxdyhdLdzf

dzdydxfdtz

Lds xy2

1 25

2222222

22

4

1

8

1 32 SYM

SYMcSYM s

TN ratioViscosity

Elliptic flow of RHIC 2.01.0 QCD

QCD

s

KSS conjecture:

4

1

sfor all fluid.

JHEP 1007:042,2010, Hou, Liu , Li , Ren

Continuum spectrum Bound sates

Correlation function from AdS/CFT

The gravity dual of a Wilson loop at large and large cN

][min)(tr CSeCW

C

xAdxi

PeCW)(

)(

the minu.area of string world

sheet in the AdS_5

Heavy quark Potential from AdS/CFT

Heavy quark potential probes confinement

hadronic phase and meson melting in plasma

line] single[2-lines] parallel[),( minmin SSTTrF

Heavy quark potential at zero temperature

q

q3x

r z

r

gNrFrV YMc

4

1

24)0,()0,(

4

22

No confinement in N=4 SYM!

The world sheet at the minimum

rzz

dxz

z 2

3

2

0 440

2

3

)2(

4

1

ith w0

The potential

Maldacena

Potential:

F-ansatz

U-ansatz

)()(

41

4),(

4

2

rrTrr

TrF c

0)( cTr

),(),( TrFTrV

T

F

TTTrTSTrFTrV 2),(),(),(

r

r

V

V

cr

cr

cr

Trc

7541.0

Rey, Theisen and YeeHeavy quark potential at a nonzero temperature

Dissociate Temperature

Hou, Ren JHEP01 (08)

Subleading order potential

Zhang,Hou, Ren,Yin JHEP07:035 （ 2011 ）Chu, Hou , Ren, JHEP08: 004 (2009)

•The coupling is not infinity

),(

2expexp][

XSi

ddXAdxiCWC

Strong coupling expansion

Semi-classical expansion

...

][0 ,][ln

Cb

XSiCW

X = the solution of the classical equation of motion;

b[C] comes from the fluctuation of the string world sheet around X

,

more significant than 3 -correction for Wilson loops.

Gravity dual of a Wilson loop at finite coupling

ijijij gggXXX 0 ,

...)()()0,(),( )2()2( FB SXSXSXS

Bosonic and fermionic fluctuations decouple.

ZeCW XiS )0,(][

With fluctuations:

FB ZZZ

)(det2

1

3

8det

4

11det

4

11-det

22

5)2(22

3

)2(22)2(22

R

RR

ZZZ FB

)()det2det(-24det

4

11det

4

11-det

22

52)2(22

1

)2(22)2(22

R

RR

Z

Partition function at finite T with fluct.

Straight line ：

Parallel lines ：

Hou, Liu, Ren, PRD80,2009

J.Math.Phys.,1,48(1960)J.Math.Phys.,40,6044(1999)[physics/9712048]

2 2 2

1 1 1

det [ , ]

det [ , ]

H u v

H u v

( , )i iu v Are 2 independent solutions 。

( ) ( ) ( ) ( )[ , ]

[ , ]i i i i

i ii i

u a v b u b v au v

W u v

Reduce evaluating functional determinants to a set of 2nd order ordinary differential equations, which are solved numerically

Wronskian determinant

Computing of the determinant ratio

Chu,Hou, Ren,JHEP0908,(2009)

2

4

4 1.33460 1( ) [1 ( )]

1( )4

V r Or

Next leading order Results

Erickson etc. NPB582,2000

Erickson etc. NPB582, 2000;

Confirmed by Forini arXiv:1009.3939

NL potential at finite T

Zhang,Hou, Ren,Yin JHEP07:035 （ 2011 ）

Summary

AdS/CFT provides a useful method to address RHIC physics at strong coupling

We calculated dissociation temperatures Td of heavy quarkonium states from AdS/CFT We computed the heavy-quark potential up to sub-leading order, confirmed by analytic calcuation by V. Forini. The strength of the potential is weakend as the 't Hooft coupling is reduced from infinity as is expected intuitively.

The applicability of these results demand phenomenological work to explain them in a way which can be translated to QCD.

QCD versus N=4 Super Yang-Mills from gravity dual

QCD Super YM

3 >>1

t’Hooft coupling 5.5-18.8 >>1

Quarks Fundamental Adjoint

Conformal symmetry NoYes at zero T

No at nonzero T

Supersymmetry NoYes at zero T

No at nonzero T

cN

Maldacena conjecture (cont.)

But N=4 SYM is not QCD! It is supersymmetric; It is conformal ( no confinement ); No fundamental quarks; It is large N_c.

---- 1, 2 may not be serious issues for QGP;

---- Attempts to add quark flavors; ---- Attempts to introduce IR cutoff.