Novel color superconducting phases of $\cal{N}$ = 4 super Yang-Mills at strong coupling

We revisit the large-$N_c$ phase diagram of $\cal{N}$ = 4 super Yang-Mills theory at finite $R$-charge density and strong coupling, by means of the AdS/CFT correspondence. We conjecture new phases that result from a black hole shedding some of its charge through the nucleation of probe color D3-branes that remain at a finite distance from the black hole when the dual field theory lives on a sphere. In the corresponding ground states the color group is partially Higgsed, so these phases can be identified as having a type of color superconductivity. The new phases would appear at intermediate values of the $R$-charge chemical potential and we expect them to be metastable but long-lived in the large-$N_c$ limit.