Clustering and decomposition for non-BPS solutions of the C PN-1 models

We look at solutions [both Bogomol'nyi-Prasad-Sommerfield (BPS) and non-BPS] of the CPN-1 model on R×S1 (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. © 2014 American Physical Society.