Heavy-quark potential at subleading order from AdS/CFT

Defu Hou

Huazhong Normal University, Wuhan

Hou, Ren, JHEP0801:029 （ 2008 ） Chu, Hou ,Ren, JHEP0908:004 (20

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

With : S. Chu, J. Liu , H. Ren

• Motivations

• Holographic potential and melting T

• Subleading order potential from AdS/CFT

• Conclusions

OUTLINES

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

Lattice: problematic with finite chemical potentioal, time-

dependent problems

Dyson-Schwinger Eq.

AdS/CFT: Notable success in RHIC physics

Motivations

AdS/CFT applied to RHIC physics

• Viscosity, /s.

• Thermodynamics.

• Jet quenching

• Photon production, Friction

• Heavy quarkonium

• Hardron spectrum (ADS/QCD)

Heavy quark potential probes the confinement in hadronic matter and meson melting in plasma

AdS/CFT at finite temperature

Classical Supergravity on AdS-BH×S5

4dim. Large-Nc strongly coupledSU(Nc) N=4 SYM at finite temperature(in the deconfinement phase).

conjecture

=

Witten ‘98 Maldacena ‘97

According to the holographic principle, the thermal average of a WL operator in 4D N=4 SUSY YM at large N_c and large 't Hooft coupling corresponds to the minimum area of the string world sheet in the 5D AdS metric with a Euclidean signature

Potential from AdS/CFT

WL at Zero T (Maldacena 98)

bounded by the loop C, when y goes to infinity, y->1 BH

Wilson-loop at finite temperature

Minimizing the world sheet area (the Nambu-Goto action)

Free energy

qq r qq r

BH

y

Result of pentential

F(r,T)

r

r0

Dissociate Temperature

Hou, Ren JHEP01 (08)

Td with deformed metric

),(

2expexp][

XSi

ddXAdxiCWC

Strong couping 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

)(xA

),(2

1

XS

55 SAdS

),( X

= the gauge potential of N=4 SUSY YM;

= the superstring action in

= the collection of bosonic and fermionic coordinates;C = a loop on the AdS boundary, z=0.

1 2

YMgNc

( Metsaev and Tseytlin)

Parallel lines ：

Straight line ：4

31 3 5

2 22 2

det ( )[ ] ln

det ( 2)det ( )

iW C

43

2 1 52 2 22 2

det ( )[ ] ln

det( 2)det ( 4 )det ( )

iW C

R

Wilson-loop at sub-leading order

)(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

Subleading order correction to potential

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 detterminant

Computing of the determinant ratio

Chu, Hou, Ren,JHEP0908,(09)

2

4

4 1.33460 1( ) [1 ( )]

1( )4

V r Or

Subleading order Results

Erickson etc. NPB582, 2000

Erickson etc. NPB582, 2000;Pineda, PRD77,02170

At finite temperature

Summary

We calculated dissociation temperatures Td of heavy quarkonium states from holographic potential ,which have remarkable features compariable with that from Lattice

We computed the heavy-quark potential up at sub-leading order

We derived the partition function of Wilson loop with fluctuations in strongly coupling N=4 SYM plasma

t

x1

z

t

z

x1

z

x1

z

-r/2 r/2

z0

Straight lin

Parallel lines: