Condensed matter physics of a strongly coupled gauge theory with quarks: some novel features of the phase diagram

We revisit the phase diagram of the N=4 SU(N_c) super-Yang-Mills theory coupled to N_f fundamental "quarks" at strong coupling using the gauge-gravity correspondence. We show that in the plane of temperature v.s. baryon chemical potential there is a critical line of third order phase transition which ends at a tricritical point after which the transition becomes first order. Close to the critical line there is an intriguing logarithmic behavior, which cannot follow from a mean field type of analysis. We argue that on the string theory side the third order phase transition is driven by the condensation of worldsheet instantons and that this transition might become a smooth crossover at finite 't Hooft coupling.