Holographic thermodynamics at finite baryon density: some exact results

We use the AdS/CFT correspondence to study the thermodynamics of massive N=2 supersymmetric hypermultiplets coupled to N=4 supersymmetric SU(N-c) Yang-Mills theory in the limits of large N-c and large 't Hooft coupling. In particular, we study the theory at finite baryon number density. At zero temperature, we present an exact expression for the hypermultiplets' leading-order contribution to the free energy, and in the supergravity description we clarify which D-brane configuration is appropriate for any given value of the chemical potential. We find a second-order phase transition when the chemical potential equals the mass. At finite temperature, we present an exact expression for the hypermultiplets' leading-order contribution to the free energy at zero mass.