Heavyquark potential at subleading order from Ad SCFT

Heavy-quark potential at subleading order from Ad. S/CFT Defu Hou Huazhong Normal University, Wuhan With : S. Chu, J. Liu , H. Ren Hou, Ren, Chu, Hou , Ren, Hou, Liu, Ren, JHEP 0801: 029（2008） JHEP 0908: 004 (2009) PRD 80: 046007 (2009)

OUTLINES • • Motivations Holographic potential and melting T Subleading order potential from Ad. S/CFT Conclusions

Motivations Many interesting phenomena in QCD lie in the strongly-coupled region. Lattice: problematic with finite chemical potentioal, timedependent problems Dyson-Schwinger Eq. Ad. S/CFT: Notable success in RHIC physics

Ad. S/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

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

Potential from Ad. S/CFT According to the holographic principle, thermal average of a WL operator in 4 D 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 5 D Ad. S metric with a Euclidean signature

WL at Zero T (Maldacena 98)

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

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

Free energy

q r q y BH

Result of pentential

F(r, T) r r 0

Dissociate Temperature Hou, Ren JHEP 01 (08)

Td with deformed metric

Gravity dual of a Wilson loop 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.

= 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 Ad. S boundary, z=0.

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

Partition function at finite T with fluct. Hou, Liu, Ren, PRD 80, 2009 Straight line： Parallel lines：

Subleading order correction to potential

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 2 nd order ordinary differential equations, which are solved numerically

Subleading order Results Chu, Hou, Ren, JHEP 0908, (09) Erickson etc. NPB 582, 2000; Pineda, PRD 77, 02170

At finite temperature

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

Straight lin t z z x 1 Parallel lines: t z z 0 x 1 z -r/2 x 1