Heavy-quark potential from AdS/CFT

1. 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

2. 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)

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

4. = conjecture AdS/CFT corerspondence 4dim. Large-Nc strongly coupled SU(Nc) N=4 SYM ( finite T). Maldacena ‘97 Witten ‘98 Type II B Super String theory on AdS-BH×S5

5. ‘t Hooft coupling

6. 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 ….. Policastro, Son and Starinet Witten Liu, Rajagopal and Wiederman Heavy quark potential probes confinement hadronic phase and meson melting in plasma

7. Shear viscosity: Policastro, Son and Starinets y The friction force per unit area x ---- Kubo formula where ---- AdS/CFT recipe: The coefficient of the term of the gravity action Elliptic flow of RHIC KSS conjecture: for all fluid.

8. Correlation function from AdS/CFT Continuum spectrum Bound sates JHEP 1007:042,2010, Hou, Liu , Li , Ren

9. The gravity dual of a Wilson loop at largeand large Heavy quark Potential from AdS/CFT the minu.area ofstring world sheet in the AdS_5 Heavy quark potential probes confinement hadronic phase and meson melting in plasma

10. Heavy quark potential at zero temperature Maldacena r z The world sheet at the minimum The potential No confinement in N=4 SYM!

11. Heavy quark potential at a nonzero temperature Rey, Theisen and Yee r Potential: V F-ansatz r U-ansatz V

12. Dissociate Temperature Hou, Ren JHEP01 (08)

13. Subleading order potential • The coupling is not infinity • Zhang,Hou, Ren,Yin JHEP07:035（2011） • Chu, Hou , Ren, JHEP08: 004 (2009)

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

15. With fluctuations: Bosonic and fermionic fluctuations decouple.

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

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

18. Next leading order Results Chu,Hou, Ren,JHEP0908,(2009) Erickson etc. NPB582,2000 Erickson etc. NPB582, 2000;

19. Confirmed by Forini arXiv:1009.3939

20. NL potential at finite T Zhang,Hou, Ren,Yin JHEP07:035（2011）

21. 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.

22. Maldacena conjecture (cont.) QCD versus N=4 Super Yang-Mills from gravity dual

23. 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.