Vacuum Mass Spectra for SU(N) Self-Dual Chern-Simons-Higgs Systems

We study the $SU(N)$ self-dual Chern-Simons-Higgs systems with adjoint matter coupling, and show that the sixth order self-dual potential has $p(N)$ gauge inequivalent degenerate minima, where $p(N)$ is the number of partitions of $N$. We compute the masses of the gauge and scalar excitations in these different vacua, revealing an intricate mass structure which reflects the self-dual nature of the model.