1. Some Issues in AdS/QCD Based on collaboration with
Sang-Jin Sin (Hanyang Univ.)
Based on collaboration with
S.Nakamura, YS.Seo, P.Yogendran (Hanyang,cquest)
BH.Lee, YM.Kim, CY.Park (Cquest, KIAS)
E.Shuryak, I.Zahed, KY.Kim (Stony Brook)

2. String Theory and Hadron physics
Invented as a Hadron theory (1GeV)
Became theory of gravity (plank scale)
back to Hadron theory with AdS/CFT
Key idea: D-brane , Open-Closed string duality(gauge/gravity)
Decoupling of Plank scale: New scale =AdS radius  t`Hooft coupling of gauge theory.

3. D-brane Open string  gauge theory Closed string gravity
D-brane=Membrane like closed string soliton whose vibration is restricted as open string vibration.

5. YM/AdS and Thermal YM / AdS-BHP
5d AdS
4d YM

6. Quarks, baryons, chemical potentials
mu=A at infinity D3 F1 Nf Nc D5
Quark=string connecting color & flavor branes
Baryon vertex
Chemical potential= tail of electricpotential

7. A few questions in RHIC//AdS
Jet quenching (with I. Zahed 2004)
Elliptic Flow (with S.Nakamura & SP. Kim,06)
Cooling and Expansion Rate (Shuryak & Zahed,05)
Calculation of dissipation in expanding Fireball (with KY.Kim & Zahed, 07)
Dense matter effect and Phase diagram (with Nakamura, Seo, Yogendran, 06)
Rapid thermalization

8. 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

9. 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?

10. 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/Nc=finite T Nf
confinement
density

11. 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.

12. Baryon chemical potential
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/ )
Horigome-Tanii (hep-th/ ) Use eq. of Motion for A_0
mu=A at infinity

13. How baryon charge appear?
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.

14. AdS charged 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

15. Back reaction of metric
Q=given baryon charge, q=parameter of RN BH
What is relation of q & Q?
ANS:

16. Thermodynamics without Hard Wall
Fixed chemical potential (grand canonical)
Fixed charge (Canonical) : add a surface term or Legendre transform
grand canonical v.s Canonical

17. Phase transitions without/with back reaction
Introducing hard wallHawking-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.

18. Phase diagram (fixed density)
With back reaction v.s Without
Main change is attributed to the def. change of T.

19. Phase diagram: chemical potential
Z. Fodor, S.D. Katz
(hep-lat/ )

20. Temperature along the phase boundary

21. conclusion
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.