Mass Degeneracies In Self-Dual Models

An algebraic restriction of the nonabelian self-dual Chern-Simons-Higgs systems leads to coupled abelian models with interesting mass spectra. The vacua are characterized by embeddings of $SU(2)$ into the gauge algebra, and in the broken phases the gauge and real scalar masses coincide, reflecting the relation of these self-dual models to $N=2$ SUSY. The masses themselves are related to the exponents of the gauge algebra, and the self-duality equation is a deformation of the classical Toda equations.