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

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: (2009)

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

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

‘t Hooft coupling

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

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

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

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

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

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

Dissociate Temperature Hou, Ren JHEP01 (08)

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

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, more significant than -correction for Wilson loops. Gravity dual of a Wilson loop at finite coupling

Bosonic and fermionic fluctuations decouple. With fluctuations:

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

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

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

Confirmed by Forini arXiv:

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

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.

QCD versus N=4 Super Yang-Mills from gravity dual QCDSuper YM 3>>1 t’Hooft coupling >>1 QuarksFundamentalAdjoint Conformal symmetryNo Yes at zero T No at nonzero T SupersymmetryNo Yes at zero T No at nonzero T Maldacena conjecture (cont.)

But N=4 SYM is not QCD! It is supersymmetric; It is conformal ( no confinement ); No fundamental quarks; It is large N_c , 2 may not be serious issues for QGP; ---- Attempts to add quark flavors; ---- Attempts to introduce IR cutoff.