We look at solutions (both BPS and non-BPS) of the $\mathbb{ CP}^{ N-1}$ model on $\mathbb{ R} \times S^1$ (with twisted boundary conditions), in particular by using a conformal mapping technique, and we show how to interpret these solutions by decomposing them into expressions describing constituent solitons. We point out the problems that may arise (for non-BPS solutions) when one naively looks at the clustering properties of these solutions. This could lead to misunderstandings when studying extrapolations between small and large compactification radii.
Categories: hep-th