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

TL;DR

This paper investigates the impact of baryon density on the gravity background in AdS/QCD models with flavor branes, revealing significant changes in phase structure and chemical potential dependence when back-reaction is fully considered.

Contribution

It demonstrates how including flavor brane back-reaction alters the phase diagram and chemical potential effects in AdS/QCD models, extending previous probe brane analyses.

Findings

Phase diagram closes at finite density with back-reaction.

Non-trivial chemical potential dependence in the confining phase.

Back-reaction effects are proportional to N_f/N_c.

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.