heavy-quark potential from ads/cft 侯 德 富 华中师范大学粒子物理研究所...
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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.