1. Quark number susceptibility with finite chemical potential in hQCD
Youngman Kim
with Y. Matsuo, W. Sim, S. Takeuchi, T. Tsukioka, arXiv: [hep-th]
(Harish-Chandra Research Institute, Samsung, APCTP)

2. Plan Why qSUS? Holographic QCD in a nutshell
qSUS with finite chemical potential
Discussion

3. Why qSUS?

4. Lattice QCD

5. Signal of CEP
(two flavor QCD)
Allton et al, Phys.Rev.D71:054508,2005

6. Cheng et al, Phys.Rev.D79:074505,2009

7. T. Kunihiro, Phys. Lett. B 271, (1991) 395

8. hQCD in a nutshell
AdS/QCD ?

9. A review: J. Erdmenger, N. Evans, I. Kirsch, E. Threlfall, Eur.Phys.J. A35:81-133,2008.

10. AdS/CFT Dictionary 4D CFT (QCD)  5D AdS
4D generating functional  5D (classical) effective action
Operator  5D bulk field
[Operator]  5D mass
Current conservation  gauge symmetry
Large Q  small z
Confinement  Compactified z
Resonances  Kaluza-Klein states

11. Example: holographic deconfinement transition
E. Witten, Adv. Theor. Math. Phys. 2, 505 (1998),
C. P. Herzog, Phys. Rev. Lett.98, (2007)
1. thermal AdS:
2. AdS black hole:
Transition between two backgrounds
(De)confinement transition

12. Example: retarded Green’s function in hQCD
Solving the EoM of the bulk field with in-falling boundary condition

15. dependent

16. From the first and second equations,
In-falling BC
Now we are to solve the EoM for F(u) in the limit of long-wave length and
low-frequency.

18. Then, we obtain

19. Following the procedure, we obtain the retarded Greens function
diffusion constant
D. T. Son, and O. Starinets, JHEP09 (2002) 042;
G. Policastro, D. T. Son, and O. Starinets, JHEP09 (2002) 043

20. qSUS with finite chemical potential

21. An AdS BH with U(1) charge
U(1) gauge symmetry in bulk  U(1) global symmetry in gauge theory side

22. A. Chamblin, R. Emparan, C. V. Johnson, and R. C. Myers, PRD (1999)
(negative specific heat)
Chemical potential
“The conformal field theory is in a thermal ensemble for which a certain U(1) charge density has also been turned on.’’
A. Chamblin, R. Emparan, C. V. Johnson, and R. C. Myers, PRD (1999)

23. For zero chemical potential, see

25. Certainly, the transition is first order due to large Nc nature of the present approach.
For small chemical potential, there is a possibility to connect low and high T smoothly with 1/Nc corrections.
For large chemical potential, there is no hope.
So, with 1/Nc corrections, the transition is like crossover for small chemical potential and first order for large chemical potential. But it is only speculation.

27. D3/D7 model

28. Discussion Finite quark mass effect? (in progress)
RN-AdS is describing QGP-like system with finite chemical potential.
What is the gravity background dual to QGP with/without density?
Generic problem is of course to collect all 1/Nc corrections in a consistent way.