Towards a Holographic Quark Matter Crystal

Understand

We construct the gravity dual of $d=4$, $\mathcal{N}=4$, SU($N_\rm{c}$) super Yang-Mills theory, coupled to $N_\rm{f}$ flavors of dynamical quarks, at non-zero temperature $T$ and non-zero quark density $N_\rm{q}$.

• The supergravity solutions possess a regular horizon if $T>0$ and include the backreaction of $N_\rm{c}$ color D3-branes and $N_\rm{f}$ flavor D7-branes with $N_\rm{q}$ 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.