  We study a heterotic two-dimensional N=(0,2) gauged non-linear sigma-model
whose target space is a weighted complex projective space. We consider the case
with N positively and N^~=N_F - N negatively charged fields. This model is
believed to give a description of the low-energy physics of a non-Abelian
semi-local vortex in a four-dimensional N=2 supersymmetric U(N) gauge theory
with N_F > N matter hypermultiplets. The supersymmetry in the latter theory is
broken down to N=1 by a mass term for the adjoint fields. We solve the model in
the large-N approximation and explore a two-dimensional subset of the mass
parameter space for which a discrete Z_{N-N^~} symmetry is preserved.
Supersymmetry is generically broken, but it is preserved for special values of
the masses where a new branch opens up and the model becomes super-conformal.
