Bulk Filling Branes and the Baryon Density in AdS/QCD with gravity back-reaction

Abstract

We consider the gravity back reaction on the metric due to the baryon density in effective ads/qcd model by reconsidering the role of the charged AdS black hole. Previously it has been known that the U(1) charge is dual to the R-charge. Here we point out that if we consider the case where $AdS_5$ is completely filled with $N_f$ flavor branes, the gravity back reaction produces charged AdS black hole where the effect of charge on the metric is proportional to $N_f/N_c$. As a consequence, phase diagram changes qualitatively if we allow $N_f/N_c$ finite: it closes at the finite density unlike the probe brane embedding approach. Another issue we discuss here is the question whether there is any chemical potential dependence in the confining phase. We consider this problem in the hard wall model with baryon charge. We conclude that there is a non-trivial dependence on the chemical potential in this case also.

Figures (3)

• Figure 1: Temperature as function of $r_+$. (a) fixed q, (b) $T$ v.s $r_+$ at the phase boundary.
• Figure 2: Phase diagrams for the fixed charge (a) and for the fixed chemical potential (b). In $q$-$T$ space, two ends points of phase boundary are given by $(q,T)=(0,2^{1/4}r_m/\pi R^2)$ and $(2.9314r_m^3/R,0)$. Below (over) the boundary is the (de-)confinement region.
• Figure 3: Phase diagrams for the fixed chemical potential with AdS without charge as the low temperature phase. (a)$r_+$ v.s $\mu$. In actual plot $r$ means $r_+/r_m$ and $\mu$ means $\mu aR/r_m$; (b) Temperature v.s chemical potential; Actual plot is $T aR/r_m$ v.s $\mu aR/r_m$. In each case, the thick line is the phase boundary and the connection point is $(T,\mu,r_+ )=( {r_m}/({2aR}),r_m/(aR),r_m)$ respectively. Notice that phase diagram closes in $T$-$\mu$ diagram.