  We explore phases of N=2 super Yang-Mills theory at finite quark density by
introducing quark chemical potential in a D3-D7 setup. We formulate the
thermodynamics of brane embeddings and find that we need to renormalize the
finite chemical potential due to the divergence of the thermodynamic potentials
and we find that the density versus chemical potential equation of state has
rich structure. This yields two distinct first order phase transitions in a
small window of quark density. In order 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 sQGP--wQGP phases of QCD.
