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Heavy-quark potential at subleading order from AdS/CFT

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)

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Heavy-quark potential at subleading order from AdS/CFT

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  1. 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) • Hou, Liu, Ren, PRD80:046007 (2009)

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

  3. Motivations 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

  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. = conjecture AdS/CFT at finite temperature Classical Supergravity on AdS-BH×S5 Maldacena ‘97 Witten ‘98 4dim. Large-Nc strongly coupled SU(Nc) N=4 SYM at finite temperature (in the deconfinement phase).

  6. Potential from AdS/CFT 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

  7. WL at Zero T (Maldacena 98)

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

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

  10. Free energy

  11. q q q r r q y BH

  12. Result of pentential

  13. F(r,T) r r0

  14. Dissociate Temperature Hou, Ren JHEP01 (08)

  15. Td with deformed metric

  16. Strong couping expansion Semi-classical expansion Gravity dual of a Wilson loop , = 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

  17. = the gauge potential of N=4 SUSY YM; = the superstring action in ( Metsaev and Tseytlin) = the collection of bosonic and fermionic coordinates; C = a loop on the AdS boundary, z=0.

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

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

  20. Subleading order correction to potential

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

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

  23. At finite temperature

  24. 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

  25. t t x1 z z z z0 z x1 x1 r/2 -r/2 Straight lin Parallel lines:

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