Towards a holographic quark matter crystal.

We construct the gravity dual of d = 4, N=4N=4 , SU(Nc) super Yang-Mills theory, coupled to Nf flavors of dynamical quarks, at non-zero temperature T and nonzero quark density Nq. The supergravity solutions possess a regular horizon if T > 0 and include the backreaction of Nc color D3-branes and Nf flavor D7-branes with Nq units of electric flux on their worldvolume. At zero temperature the solutions interpolate between a Landau pole singularity in the ultraviolet and a Lifshitz geometry in the infrared. At high temperature the thermodynamics is directly sensitive to the Landau pole, whereas at low temperature it is not, as expected from effective field theory. At low temperature and sufficiently high charge density we find thermodynamic and dynamic instabilities towards the spontaneous breaking of translation invariance