1. With Y. Seo, J.P. Shock, D. Zoakos(0911.xxxx) CY.Park, KH. Jo, BH Lee( 0909.3914 )

2.  A good way summarizing the effect of the interaction.  Brown and Rho: m* goes lower.  Based on tendency near chiral restoration.  C14 and other remarkable applications.   Yet. No observable support.  Lattice calculation with density is still difficult.  So, need new idea. 2009-10-31 0910HIM-WCU 2

3. 2009-10-31 3 0910HIM-WCU

4.  Gluon dynamics is replaced by AdS5.  Flavor dyn. By space filling branes.  Meson=fluctuation of branes. 2009-10-31 0910HIM-WCU 4

5. Global symmetry Boundary AdS/CFT gauge symmetry Bulk Local charge 2009-10-31 0910HIM-WCU 5

6.  Q=given baryon charge, q=parameter of RN BH  relation of q & Q? 2009-10-31 0910HIM-WCU 6

7. 2009-10-31 0910HIM-WCU 7 Chamblin et.al hep-th/9902170: with Q asR charge Here It is consequence of the back reaction and Q=baryon charge Remark: this is for deconfined phase.

8.  Dual to MIT bag-Model  In/Out is switched in ads/cft  Cut off r >r_m  Use z=1/r 2009-10-31 0910HIM-WCU 8

9. 2009-10-31 0910HIM-WCU 9 Z. Fodor, S.D. Katz Z. FodorS.D. Katz (hep-lat/0106002)

10.  With back reaction v.s Without 2009-10-31 0910HIM-WCU 1010 Main change is attributed to the def. change of T.

11. 2009-10-31 0910HIM-WCU 1111

12. 2009-10-31 0910HIM-WCU 1212 Decay constants

13. 2009-10-31 0910HIM-WCU 1313

14. 2009-10-31 0910HIM-WCU 1414 

15. 2009-10-31 0910HIM-WCU 1515

16. 2009-10-31 0910HIM-WCU 1616

17. 2009-10-31 0910HIM-WCU 1717

18. 2009-10-31 0910HIM-WCU 1818

19. 2009-10-31 0910HIM-WCU 1919 Pion mass rho mass BR-scaling is not there in bottom up approach. Caveat: coupling to the metric fluctuation is not included.

20.  Matter with probe brane  2009-10-31 0910HIM-WCU 2020

21. 2009-10-31 0910HIM-WCU 2121 Black D3 quark

22. 2009-10-31 0910HIM-WCU 2222 How mesons behave on this configuration?

23. 2009-10-31 0910HIM-WCU 2323 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

24.  Theoretical equipments are actions and eq. of M  How D-branes vibrate : DBI 2009-10-31 0910HIM-WCU 2424

25. We consider D7 brane as a probe brane where the other end point of fundamental strings are attached  End point can be regarded as point source on D7 brane 2009-10-31 0910HIM-WCU 2525  Induced metric on D7 brane  DBI action

26. 2009-10-31 0910HIM-WCU 2626  Equation of motion for  Legendre transformed Hamiltonian

27. 2009-10-31 0910HIM-WCU 27

28. 2009-10-31 0910HIM-WCU 2828

29.  For dense matter we need D5.  Add baryon vertices in uniform fashion along D3 direction (spacial direction). Remark: For single or non-uniform density distribution It is difficult. 2009-10-31 0910HIM-WCU 2929

30. 2009-10-31 0910HIM-WCU 3030  Baryons : D5 brane wrapped on an S 5 on which N c F1’s terminate  The background 5-form field strength can couple to the world volume U(1) gauge field via Chern-Simons term  DBI action for single D5 brane with Nc F1’s  Induced metric on D5 brane

31. ν Nc F1’s are attached at south pole and (1- ν)Nc F1’s at north pole 2009-10-31 0910HIM-WCU 3131  Dimensionless Displacement  Equation of motion and solution  Legendre transformed Hamiltonian

32. 2009-10-31 0910HIM-WCU 3232  D5 brane solution  Force at cusp D4/D6(D3/D5) YS, S Sin, JHEP 0804:010, 2008

33. 2009-10-31 0910HIM-WCU 3333  Total configuration(Baryon D5 + F1’s +probe D7) can be stationary if there is force balance condition  Force balance condition

34. 2009-10-31 0910HIM-WCU 3434

35. 2009-10-31 0910HIM-WCU 3535

36. 2009-10-31 0910HIM-WCU 3636

37. 2009-10-31 0910HIM-WCU 3737  Deformation of D-brane Deformation of D5 braneBaryon mass Deformation of D7 braneBaryon-baryon interaction  Density dependence of baryon mass mq = 1.5 mq = 1 mq =0 D4/D6(D3/D5) YS, S Sin, JHEP 0804:010, 2008

38. 2009-10-31 0910HIM-WCU 3838 Asymptotic behavior of D7 brane Chiral condensation

39.  Scalar fluctuation 2009-10-31 0910HIM-WCU 3939 Second order Lagranian with quardratic terms for fluctuation Equation of motion for fluctuation

40.  Effective potential 2009-10-31 0910HIM-WCU 4040

41.  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. 2009-10-31 0910HIM-WCU 4141

42. 2009-10-31 0910HIM-WCU 4242

43.  BR scaling is possible for some model for appreciable quark mass, while it is not there in some of the model.  Remark: So are we are still in pion mode. Vector mode will be reported in future. (Rho Seo SJS) 2009-10-31 0910HIM-WCU 4343

44.  Here, we studied Density dependences.  Following objects are calculable in hqcd:  0.Phase diagram (not critical point/crossover).  1. equation of state.  2. all Thermodnamic quantities.  3. condensations (chiral, gluon, meson … )  4. susceptiblities. compressibility  5. spectral functions.  6. Symmetry energies.  7. Differnet models and Different modes.  Etc ……. 2009-10-31 0910HIM-WCU 4444