On holographic phase transitions at finite chemical potential

Recent Holographic studies have shown that N=4 super Yang-Mills theory coupled to fundamental matter with finite chemical potential undergoes a first order phase transition. In this paper, we study Nf D6 probe branes with or without electric field on it in the black D4 brane background compactified on a circle with supersymmetry breaking boundary condition. At energy scales much lower than the compactification scale, the dual gauge theory is effectively four dimensional non-supersymmetric SU(Nc) Yang-Mills theory coupled to fundamental matter with or without baryon number charge. Within the supergravity approximation, the decoupling of the Kaluza-Klein modes is not fully realized. For chemical potential mu<NcMq there is a line of first order phase transitions from stable meson phase to unstable meson phase. On the other hand for mu>NcMq there is no phase transition and mesons are unstable. A peculiar and interesting property of this system is that for a certain range of chemical potential mu<NcMq, a new phase transition appears in the unstable meson phase. This phase transition is characterized by a discontinuous change of unstable meson lifetime.