Based on collaboration withS.Nakamura, YS.Seo, P.Yogendran (Hanyang,cquest)

BH.Lee, YM.Kim, CY.Park (Cquest, KIAS)E.Shuryak, I.Zahed, KY.Kim (Stony Brook)

Some Issues in AdS/QCD

Sang-Jin Sin (Hanyang Univ.)2007.11.30 @HYU

String Theory and Hadron physics1. Invented as a Hadron theory (1GeV) 2. Became theory of gravity (plank scale)3. back to Hadron theory with AdS/CFT4. Key idea: D-brane ,

Open-Closed string duality(gauge/gravity) 5. Decoupling of Plank scale: New scale

=AdS radius t`Hooft coupling of gauge theory.

D-brane Open string gauge theory Closed string gravity D-brane=Membrane like closed string

solitonwhose vibration is restricted as open string vibration.

YM/AdS andThermal YM / AdS-BH

P

1/ T5d AdS

4d YM

Quarks, baryons, chemical potentials

mu=A at infinity

Nf

Nc

D5

D3

F1

Quark=string connecting color & flavor branes

Chemical potential= tail of electricpotential

Baryon vertex

A few questions in RHIC//AdS1. Jet quenching (with I. Zahed 2004)2. Elliptic Flow (with S.Nakamura & SP.

Kim,06)3. Cooling and Expansion Rate (Shuryak &

Zahed,05)4. Calculation of dissipation in expanding

Fireball (with KY.Kim & Zahed, 07)5. Dense matter effect and Phase diagram

(with Nakamura, Seo, Yogendran, 06)6. Rapid thermalization

In the rest of this talk I will pick up one issue and give some

details .

Phase diagram in Temperature-Density plane

Back reaction of geometry to the dense matter is essential. With and only with BR, Phase diagram closes

Deconfinement Phase Transition 1. Without Matter: Hawking Page Transition

between Two competing geometries: AdS with IR cutoff (Low T) & AdS BH (High T)

2. what if there is baryon chage?

Problem in Probe brane description Large Nc and finite Nf: little effect of baryon/quark density in phase

transition and P.D is OPEN

Nf T

density

confinement

Nf/Nc=finite

Origin of the problem Nf/Nc ~ 1 in QCD.

Since Nc has to be large for AdS/CFT, so is the Nf. Then gravity back reaction is not an option but an essential.

back reaction closes phase diagram.

Baryon is not adjoint Rep. not a Bulk Field.

Chemical potential in 4d is a constant A0. Therefore mu= Tail of BRANE-FIELD A0.

(Kim-Sin-Zahed : hep-th/0608046) Horigome-Tanii (hep-th/0608198)

Use eq. of Motion for A_0

mu=

A a

t infinity

a brane U(1) charge

If Brane is Filling entire AdS 5 brane charge= bulk charge.

Since there is a unique way a U(1) charge can couple to the metric, U(1)_B charge must be related to the charge parameter in RN black hole.

Chamblin et.al hep-th/9902170:

Q identified as R charge

Bulk field A sourced by Adjoint representation

Bulk=Brane R charge and Q play the same role

Q=given baryon charge, q=parameter of RN BH What is relation of q & Q?

ANS:

Fixed chemical potential (grand canonical)

• Fixed charge (Canonical) : add a surface term or Legendre transform

• grand canonical v.s Canonical

Introducing hard wallHawking-Page Transition (Herzog)

High temperature: charged ads BH Low temperature: AdS with charges at the wall

for fixed charge case Treat the grand canonical as Legendre Tr.

Of canonical case.

With back reaction v.s Without

Main change is attributed to the def. change of T.

Z. Fodor, S.D. Katz (hep-lat/0106002)

1. We seem to have phase diagram that mimic that of QCD.

2. We seems to have correct formalism to include the baryon density in bottom up approach.

3. How mass and chiral condensation, coupling etc. are running in density?

UNDER PROgress.