1. 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 (2009) Hou, Liu, Ren, PRD80:046007 (2009) With : S. Chu, J. Liu, H. Ren

2. Motivations Holographic potential and melting T Subleading order potential from AdS/CFT Conclusions OUTLINES

3. 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

4. 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

5. AdS/CFT at finite temperature Classical Supergravity on AdS-BH×S 5 4dim. Large-Nc strongly coupled SU( Nc ) N=4 SYM at finite temperature (in the deconfinement phase). conjecture = Witten ‘98 Maldacena ‘97

6. 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

7. WL at Zero T (Maldacena 98)

9. bounded by the loop C, when y goes to infinity, y->1 BH Wilson-loop at finite temperature

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

11. Free energy

12. qq rq qr BH y

13. Result of pentential

14. F(r,T) r r0r0

15. Dissociate Temperature Hou, Ren JHEP01 (08)

16. Td with deformed metric

17. Strong couping expansion Semi-classical expansion = the solution of the classical equation of motion; b[C] comes from the fluctuation of the string world sheet around, more significant than -correction for Wilson loops. Gravity dual of a Wilson loop

18. = 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. ( Metsaev and Tseytlin)

19. Parallel lines ： Straight line ： Wilson-loop at sub-leading order

20. Partition function at finite T with fluct. Straight line ： Parallel lines ： Hou, Liu, Ren, PRD80,2009

21. Subleading order correction to potential

22. J.Math.Phys.,1,48(1960) J.Math.Phys.,40,6044(1999)[physics/9712048] Are 2 independent solutions 。 Reduce evaluating functional determinants to a set of 2nd order ordinary differential equations, which are solved numerically Wronskian detterminant Computing of the determinant ratio

23. Chu, Hou, Ren,JHEP0908,(09) Subleading order Results Erickson etc. NPB582, 2000 Erickson etc. NPB582, 2000; Pineda, PRD77,02170

24. At finite temperature

25. 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

26. t x1x1 z t z x1x1 z x1x1 z -r/2 r/2 z0z0 Straight lin Parallel lines: