1. Heavy Quarkonium States with the Holographic Potential Defu Hou (CCNU) From Strings to Things, Seattle, May 2008 With Hai-cang Ren, JHEP 0801:029,2008. 0710.2639

2. OUTLINES  Introduction  Holographic potential model from AdS/CFT  Holographic potential model with IR cut.  Concluding remarks

3. Many interesting phenomena in QCD lie in the strongly-coupled region. Non-perturbative methods for analysis Lattice: problematic with finite chemical potentioal, time- dependent problems AdS/CFT: Notable success in RHIC physics Viscosity, Jet quenching, … Introduction

4. QCD Diagramm

5. Heavy meson melting At T<Tc, confined,potenial linearing rises At T>Tc, deconf. Short range attraction range: screening length L sc As T ↗, L sc ↘, there exists a T d : the potential no longer binding for T>T d ( Melting Temperature) Heavy quakonium melting is an important signal of QGP

6. Nonperturbative calculation of T d Potential model Lattice F. Karsch, Brambilla… AdS/CFT Maldacena, Rey, Liu, Avramis Spectral function Lattice Karch AdS/CFT Hoyos, Kim et al

7. Holographic potential model from AdS/CFT

8. Q Q r 1/T t Extracting V(r) from Wilson loop

9. F(r,t) is the free energy excess of a static pair of qq The internal energy reads

10. F-ansatz V(r) =F(r,T) U –ansatz V(r)=U(r, T)

11. Poential From Lattice Quarkonium probes non-perturbative information about medium. How? Wilson loop is static time-like and in fundamental representation: Wilson loop is calculable in lattice QCD Bielefeld Group, hep-lat/0509001 time distance L L time Matsui, Satz 1986

12. Field Theory Gravity Theory = Gauge Theories QCD Quantum Gravity String theory the large N limit Supersymmetric Yang Mills Gravitational theory in 10 dimensions N large Calculations Correlation functions Quark-antiquark potential Holography

13. Potential from AdS/CFT According to the holographic principle, the thermal average of a Wilson loop 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,

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

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

17. qq rq qr BH + _ y

18. Free energy

19. Result of pentential

21. Bound state & Schrődinger equation

22. Numerical Results Value of ‘t Hooft coupling. Upper limit : QCD value of coupling at RHIC Lower limit: heavy quark potential, (Gubser) Mc=1.65Gev, Mb=4.85Gev, Tc=186MeV

23. Dissociate Temperature Td in MeV

24. Holographic potential model with an IR cutoff Hard Wall : Erlich, Katz, Son, Stephanov

25. In the hadronic phase In the plasma phase

26. Soft-wall model 1 : Karch, Katz, Son, Stephanov A dilaton is introduced, Metrics are the same. Soft-wall model 2 : Andreev,Zakharov;Kajantie modify string frame metric by a conformal factor

27. Free energy

29. Td with deformed metric

30. AdS/CFT and Lattice

31. Summary To assess the validity. At melting temperature of U satz We calculated dissociation temperatures Td of heavy quarkonium states from holographic potential The computed Td have remarkable features compariable with that from Lattice

32. Thanks for your attention!