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.)

Start with IIB super-string of 10 D1. 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 confinementmagnetic gauge condensate string tention∝

(Wilson loop)

[GY, Evans]

[

] )

U(1) Breaking

Then

After getting w(ρ), the meson spectra are obtained from the fluctuations of the fields in D7 brane action

[Evans]

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

Extend to finite temperature

[Erlich-Katz-Son-Stephanov][Rold-Pomarol]

[Braga IR brane glueball]

[Evans D7 induced action]

• 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

Mass Spectrum

(ii) Boundary conditions are taken as(i) For any field φ, we assume

*Improved in D7 induced action Evans

Mild T-dep

mild the enhancement near zm (ii)

Red line shows the section chosen

[Son-Starinets]The stability condition is given as

Stable region

confinement

QGP Red line shown in the Fig.(A)

The critical temperature and Phase diagram is given as follows

Meson spectrum

1.

2. Solve the profile function v(z)

3. Solve the EOM of fluctuations

Mass is controlled

(0< z <zm)

The κdep of

for T=40MeV

Under the boundary condition

Estimated on the critical line

1.

2.

on the critical curve

This is seen along two paths

(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.

This could resolve the singularity of v(z) at T= Tc

We must go back to D3/D7 string theory

[Evans]