1. Contents: １. Introduction/ Model ２． Meson Properties at Finite Temperature ３． Chemical Potential/ Phase Diagram ４． Summary Trento 06/June 20 Holographic Model for Mesons at Finite Temperature K.G, A. Nakamura, M. Yahiro, M, Tachibana, N. Uekusa, hep-ph/0512289, 0605026 Kazuo Ghoroku (Fukuoka Inst. of Tech.)

2. Start with IIB super-string of 10 D 1. Introduction N=4 SYM is not QCD we must deform AdS5 And we find a solution which leads to quark confinement Strong coupling at IR region confinement magnetic gauge condensate string tention ∝ (Wilson loop) [GY, Evans]

3. [ ] ) U(1) Breaking

4. Then After getting w(ρ), the meson spectra are obtained from the fluctuations of the fields in D7 brane action [Evans]

5. solutions for w(ρ) (with various parameters (mq,c)) ２． There is a minimum of r [GY, Evans et al] Under the conditions(i)D3/D7 repulsion, (ii)SUSY breaking on D7 Results

6. Extend to finite temperature [Erlich-Katz-Son-Stephanov] [Rold-Pomarol] [Braga IR brane glueball] [Evans D7 induced action]

9. c is assumed to be independent of T here v(z) has a logarithmic divergence c(T) will cure the second point, but now we can not extend the above solution to T Tc The two parameters are fixed as Profile v(z) and CSB

10. Mass Spectrum (ii) Boundary conditions are taken as (i) For any field φ, we assume *Improved in D7 induced action Evans

12. Mild T-dep

13. mild the enhancement near zm(ii )

20. Red line shows the section chosen [Son-Starinets] The stability condition is given as Stable region

21. confinement QGP Red line shown in the Fig.(A) The critical temperature and Phase diagram is given as follows

22. Meson spectrum 1. 2. Solve the profile function v(z) 3. Solve the EOM of fluctuations Mass is controlled (0< z <zm)

23. The κdep of for T=40MeV

25. Under the boundary condition Estimated on the critical line

26. 1. 2. on the critical curve This is seen along two paths

27. (i) are consistent with chiral perturbation [Toulban] (ii) 2. (generalized) GOR relation is good 1. T-dependences are consistent with the other approaches 4. Chemical potential induced by R-charges leads to a phase diagram similar to the one expected in QCD 3.

28. This could resolve the singularity of v(z) at T= Tc We must go back to D3/D7 string theory [Evans]