Heavy Quarkonium States with the Holographic Potential

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

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

3. Introduction 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, …

4. QCD Diagramm

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

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

7. Holographic potential model from AdS/CFT

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

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? Matsui, Satz 1986 • Wilson loop is static time-like and in fundamental representation: • Wilson loop is calculable in lattice QCD time Bielefeld Group, hep-lat/0509001 Ltime L distance

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

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. q q q r r q y _ + BH

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

32. Thanks for your attention!