Superconducting instabilities of R-charged black branes

We explore superconducting instabilities of black branes in SO(6) gauged supergravity at finite temperature and finite R-charge densities. We compute the critical temperatures for homogeneous neutral and superconducting instabilities in a truncation of 20 scalars and 15 gauge fields as a function of the chemical potentials conjugate to the three U(1) charges in SO(6). We find that despite the imbalance provided by multiple chemical potentials there is always at least one superconducting black brane branch, emerging at a temperature where the normal phase is locally thermodynamically stable. We emphasise that the three-equal charge solution, Reissner-Nordstrom, is subdominant to a thermodynamically unstable black brane at sufficiently low temperatures --- a feature which is hidden in an equal charge truncation.