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Quark number susceptibility with finite chemical potential in hQCD

Quark number susceptibility with finite chemical potential in hQCD. Youngman Kim. with Y. Matsuo, W. Sim, S. Takeuchi, T. Tsukioka, arXiv:1001.5343[hep-th] (Harish-Chandra Research Institute, Samsung, APCTP). Plan. Why qSUS? Holographic QCD in a nutshell

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Quark number susceptibility with finite chemical potential in hQCD

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  1. Quark number susceptibility with finite chemical potential in hQCD Youngman Kim with Y. Matsuo, W. Sim, S. Takeuchi, T. Tsukioka, arXiv:1001.5343[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, 091601 (2007) 1. thermal AdS: 2. AdS black hole: (De)confinement transition Transition between two backgrounds

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

  13. dependent

  14. 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.

  15. Then, we obtain

  16. 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

  17. qSUS with finite chemical potential

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

  19. (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)

  20. For zero chemical potential, see

  21. 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.

  22. D3/D7 model

  23. 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.

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