Topological susceptibility and string tension in the lattice CPN-1 models.

In the lattice CP models we studied the problems related to the measure of observables closely connected to the dynamically generated gauge field, such as the topological susceptibility and the string tension. We perfomed numerical simulations at N = 4 and N = 10. In order to test the universality, we adopted two different lattice formulations. Scaling and universality tests led to the conclusion that at N = 10 the geometrical approach gives a good definition of lattice topological susceptibility. On the other hand, N = 4 proved not to be large enough to suppress the unphysical configurations, called dislocations, contributing to χgt (at least up to ξ ≃ 30 in our lattice formulations). We obtained other determinations of χt by the field theoretical method, wich relies on a local definition of the lattice topological charge density, and the cooling method. They gave quite consistent results, showing scaling and universality. The large-N expansion predicts an exponential area law behavior for sufficiently large Wilson loops, which implies confinement, due to the dynamical matter fields and absence of the screening phenomenon. We determined the string tension, without finding evidence of screening effects.