Instability of N=2 gauge theory in compact space with an isospin chemical potential

We investigate N=2 super-Yang-Mills theory on a three sphere in the presence of an isospin chemical potential at strong coupling using the AdS/CFT correspondence. This system exhibits an instability for sufficiently large values of the chemical potential. In contrast to other related models, the first excitation to condense is not a vector meson but rather a scalar charged under the global SO(4) symmetry group. Furthermore, the spectrum of fluctuations exhibits an interesting cross-over behaviour as a function of the dimensionless temperature. We construct the new ground state of the non-linear theory.