Heavy Quarkonium melting with Holographic Potential Defu Hou (CCNU,Wuhan) SQM2008, Beijing, Oct. 6-10, 2008 With Hai-cang Ren, JHEP 0801:029,2008.

Motivations Potential from AdS/CFT Heavy quarkonium melting T Summary OUTLINES

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, … Motivation

QCD Diagramm

AdS/CFT now being applied to RHIC physics Viscosity,  /s. EOS Jet quenching “ Sound ” waves Photon production Friction … Heavy quarkonium Hardron spectrum (ADS/QCD)

Heavy meson melting At T<Tc, confined,potenial linearing rises At T>Tc, deconfined, 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 See the talk by H. Satz on Oct.7

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

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

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

F-ansatz V(r) =F(r,T) U –ansatz V(r)=U(r, T)=F+T S

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/ time distance L L time Matsui, Satz 1986

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

Potential from AdS/CFT According to the holographic principle, the thermal average of a WL operator in 4D N=4 SYM 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.

WL at Zero T (Maldacena 98)

Euler Lagrangian EQ Solution,

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

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

qq rq qr BH + _ y

Free energy

Result of pentential

F(r,T) r r0r0

Bound state & Schrődinger equation

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

Dissociation Temperature Hou, Ren JHEP01 (08)

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

In the hadronic phase In the plasma phase

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

Free energy

Td with deformed metric

AdS/CFT and Lattice

Summary We calculated dissociation temperatures Td of heavy quarkonium states from holographic potential The computed Td have remarkable features compariable with that from Lattice But N=4 SYM is not real QCD with less stronger screening