We investigate the features of ${ \rm CP}^{ N-1}$ models concerning confinement and topology. In order to study the approach to the large-$N$ asymptotic regime, we determine the topological susceptibility and the string tension for a wide range of values of $N$, in particular $N=4,10,21,41$. Quantitative agreement with the large-$N$ predictions is found for the ${ \rm CP}^{ 20}$ and the ${ \rm CP}^{ 40}$ models. Problems related to the measure of the topological susceptibility and the string tension on the lattice are discussed.
Categories: hep-lat