Mass splittings from symmetry obstruction

The long-range fields associated with non-abelian vortices generally obstruct full realization, in the spectrum, of the symmetry of the ground state. In the context of 2 + 1 dimensional field theories, we show how this effect manifests itself concretely in altered conditions for the angular momentum and in the energy spectrum. A particularly interesting case is supersymmetry, which is obstructed by the gravitational effect of any mass.