1. Holographic Hadrons in dense medium Sang-Jin Sin (HYU) @YITP 2010.3.3

2. Maldacena Phenomena A legend in our generation hep-th/9711200 Adv.Theor.Math.Phys.2:231-252,1998 The Large N limit of super conformal field theories and super-gravity. Juan Martin Maldacena, Cited 6634 times Juan Martin Maldacena, Cited Weinberg model : cited 7000 times for 40 years. 2010-3-3 NF-QCD @ Kyoto 2

3. Why? Ads/cft seems to connect string theory to many other branches of physics like *QCD, *CMT, Including QHE, High Tc SC, Graphene Not difficult to predict what will happen next 10 years! 2010-3-3 NF-QCD @ Kyoto 3

4. Defect and hope Large N, 4 SUSY, Extra degree of freedom…… Far from the reality. Nevertheless ….. After 35 years of qcd, strong interaction regime is still in mystery. Any field theory calculation is casted by doubt. Asymptotic freedom is not useful at all for the nuclear physics. Hope is overwhelming the Difference at this moment. 2010-3-3 NF-QCD @ Kyoto 4

5. Origin: D-brane 2010-3-3 NF-QCD @ Kyoto pictures by Gubser 5

6. Ads & RN Black hole 2010-3-3 NF-QCD @ Kyoto pictures by S. Gubser 6

7. Phase diagram of qcd 2010-3-3 NF-QCD @ Kyoto 7

8. Motive from Heavy Ion collision 2010-3-3 NF-QCD @ Kyoto 8 Deconfined. Original degree of freedom of qcd. But experiment shows still strongly interacting. perfect theoretical setting for ads/qcd

9. Heavy ion collision 2010-3-3 NF-QCD @ Kyoto 9

10. Elliptic flow,perfect fluidity, sqgp 2010-3-3 NF-QCD @ Kyoto 1010

11. Finite Temperature  BH 2010-3-3 NF-QCD @ Kyoto 11

12. Expanding QGP and Elliptic Flow (Nakamura, Kim, SJS 2006) 2010-3-3 NF-QCD @ Kyoto 1212

13. Difficulties for Hadrons Need New effective degrees of freedom Emergence of a Scale: Lambda QCD what caused it? Gluon condensation? Confinement Chiral symmetry breaking 2010-3-3 NF-QCD @ Kyoto 1313

14. Confinement. scale Need a scale of scale inv. Theory (qcd) MIT bag-Model In ads/qcd, 1. Hard wall ads/cft  discrete glueball spectrum 2. Witten bubble : double wick rotation of BH  area law. 2010-3-3 NF-QCD @ Kyoto 1414

15. Evidence for confining metric Wilson Loop : Area law? Yes for both. (for pure N=4 YM, Coulomb) Polyakovloop : Zero ? Yes Appearance of scale: in qcd: T and very different In hqcd: integration constant. T and equal putting. 2010-3-3 NF-QCD @ Kyoto 1515

16. Adding Matter with probe brane 2010-3-3 NF-QCD @ Kyoto 1616

17. Baryon Chemical potential Global symmetry Boundary AdS/CFT gauge symmetry Bulk Local charge 2010-3-3 NF-QCD @ Kyoto 17

18. Pauli in AdS 1. Classical Physics does not encode fermi-statistics. We are dealing with QM system. 2. In boundary we have global U(1) Q. We have a local Coulomb repulsion in AdS. What is its dual in boundary? Suggestion: Dual of the local repulsion is the Pauli effect. A classical realization of quantum statistics. Evidence: i. RN AdS shows fermionicC_v =a T. (Zahed,sjs) ii. Baryon Density dependence of the free energy. (Zahed,sjs) iii. Brane dynamics for strange matter (Y.Kim. Y.Seo. Sjs) 2010-3-3 NF-QCD @ Kyoto 1818

19. Chemical potential with Baryon 2010-3-3 NF-QCD @ Kyoto How mesons behave on this configuration? 1919

20. Holographic Hadrons in a Confining Finite Density Medium (0912.4013) Y. Seo, J. Shock, D. Zoakos +SJS Consider the situation where confinement, gluon condensation, finite baryon density are implemented. But T=0. Ask how the meson/baryon spectrum depends on the density? 2010-3-3 NF-QCD @ Kyoto 2020

21. Background geometry 2010-3-3 NF-QCD @ Kyoto Gubser’s background Non supersymetric extension of D3-D(-1) bound system Supersymmetry and chiral symmetry is broken r 0 is proportional to the gluon condensation in gauge theory This geometry support confining phase 2121

22. D7 embedding 2010-3-3 NF-QCD @ Kyoto 2222

23. Shape of Baryon vertex 2010-3-3 NF-QCD @ Kyoto  D5 brane solution  Force at cusp D4/D6(D3/D5) YS, S Sin, JHEP 0804:010, 2008 2323

24. Interaction of D7-D5: force balance with Baryon vertex 2010-3-3 NF-QCD @ Kyoto (Baryon D5 + F1’s +probe D7) can be stationary if Force balance condition is fulfilled 2424

25. 2010-3-3 NF-QCD @ Kyoto 2525

26. Baryon mass with density 2010-3-3 NF-QCD @ Kyoto  Deformation of D-brane Deformation of D5 braneBaryon mass Deformation of D7 braneBaryon-baryon interaction  Density dependence of baryon mass 2626

27. Meson: Fluctuation on D7 brane Scalar fluctuation 2010-3-3 NF-QCD @ Kyoto Second order Lagranian with quardratic terms for fluctuation Equation of motion for fluctuation 2727

28. Fluctuation on D7 brane By using shooting method, we can calculate mass spectrum of fluctuation, which is meson. For large enough quark mass, meson mass decreases! In such case BR-scaling exist. 2010-3-3 NF-QCD @ Kyoto 2828

29. For very small quark mass: 2010-3-3 NF-QCD @ Kyoto 2929

30. Chiral symmetry breaking In top down: chiral condensation is probe brane’s tail curvature in mass direction. Even for the U(1) chiral symmetry as a rotation, it is impossible to restore it by density. For non-abelian chiral symmetry  SS model, 1. v. hard to treat chiral-condensation itself. if not impossible. No room to allow mass. 2. chiral and deconfinement transition for max. separ. Here, we use bottom up (EKSS) with gravity back reaction included. 2010-3-3 NF-QCD @ Kyoto 3030

31. Analogy: h-superconductor 2010-3-3 NF-QCD @ Kyoto 3131

32. Abelian higgs in ads Couple the abelian higgs model to gravity. Set zero potential apart from the mass term determined by the conformal dimension of the excitations 2010-3-3 NF-QCD @ Kyoto 3232

33. Condensation 2010-3-3 NF-QCD @ Kyoto 3333

34. [S.C v.s Chiral] transition Supersonducting  Normal state BH with scalar hair  BH without hair Question: Can we discuss chiral transition using similar idea? Yes. We can. Star v.s BH transition. 2010-3-3 NF-QCD @ Kyoto 3434

35. Set up 2010-3-3 NF-QCD @ Kyoto 3535

36. Boundary conditions 2010-3-3 NF-QCD @ Kyoto 3636

37. Numerical results (Y.Ko+sjs) 2010-3-3 NF-QCD @ Kyoto 3737

38. What next? Here, we studied Density dependences. Following objects are calculable in hqcd: 0.Phasediagram (not critical point/crossover). 1. equation of state. 2. all Thermodnamic quantities. 3. condensations (chiral and gluon meson … ) 4. susceptiblities 5. spectral functions. 6. Symmetry energies. 7. Differnet models and Different modes. Etc ……. 2010-3-3 NF-QCD @ Kyoto 3838

39. Conclusion AdS/CFT connects string theory to many other branch of physics especially qcd. dense matter theory in qcd by ads/cft is especially useful since the correspondence is most clear and not much has been done in lattice. 2010-3-3 NF-QCD @ Kyoto 3939