  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.
