heavy-quark potential at subleading order from ads/cft
DESCRIPTION
Heavy-quark potential at subleading order from AdS/CFT. Defu Hou. Huazhong Normal University, Wuhan. With : S. Chu, J. Liu , H. Ren. Hou, Ren, JHEP0801:029 ( 2008 ) Chu, Hou ,Ren, JHEP0908:004 (2009) - PowerPoint PPT PresentationTRANSCRIPT
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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
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• Motivations
• Holographic potential and melting T
• Subleading order potential from AdS/CFT
• Conclusions
OUTLINES
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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
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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
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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
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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
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WL at Zero T (Maldacena 98)
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bounded by the loop C, when y goes to infinity, y->1 BH
Wilson-loop at finite temperature
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Minimizing the world sheet area (the Nambu-Goto action)
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Free energy
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qq r qq r
BH
y
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Result of pentential
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F(r,T)
r
r0
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Dissociate Temperature
Hou, Ren JHEP01 (08)
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Td with deformed metric
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),(
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
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)(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)
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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
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)(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
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Subleading order correction to potential
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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
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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
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At finite temperature
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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
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t
x1
z
t
z
x1
z
x1
z
-r/2 r/2
z0
Straight lin
Parallel lines: