A new phase at a finite quark density from AdS/CFT

We explore the phases of the N = 2 super Yang-Mills theory at a, finite quark density by introducing a quark chemical potential in a D3-D7 setup. We formulate the thermodynamics of brane embeddings and we find that the density versus chemical potential equation of state has a rich structure. This yields two distinct first-order phase transitions in a small window of the quark density. In other words, there is a new first-order phase transition in the region of deconfined quarks. In this new phase, the chemical potential is a decreasing function of the density. We suggest that this might be relevant to the difference in the sQGP-wQGP phases of QCD.