Holographic phase transitions at finite baryon density

We use holographic techniques to study SU(N-c) super Yang-Mills theory coupled to N-f << N-c flavours of fundamental matter at finite temperature and baryon density. We focus on four dimensions, for which the dual description consists of N-f D7-branes in the background of N-c black D3-branes, but our results apply in other dimensions as well. A non-zero chemical potential mu(b) or baryon number density n(b) is introduced via a nonvanishing worldvolume gauge field on the D7-branes. Ref. [1] identified a first order phase transition at zero density associated with 'melting' of the mesons. This extends to a line of phase transitions for small n(b), which terminates at a critical point at finite n(b). Investigation of the D7-branes' thermodynamics reveals that (partial derivative mu(b)/partial derivative n(b))(T) < 0 in a small region of the phase diagram, indicating an instability. We comment on a possible new phase which may appear in this region.