TOPOLOGICAL SUSCEPTIBILITY AND STRING TENSION IN THE LATTICE CP(N-1) MODELS

In the lattice CP(N - 1) models we study 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 perform numerical simulations at N = 4 and N = 10. In order to test the universality, we adopt two different lattice formulations. Scaling and universality tests lead to the conclusion that at N = 10 the geometrical approach gives a good definition of lattice topological susceptibility. On the other hand, N = 4 proves not to be large enough to suppress the unphysical configurations, called dislocations, contributing to chi(t)g (at least up to xi congruent-to 30 in our lattice formulations). We obtain other determinations of chi(t) by the field-theoretical method, which relies on a local definition of the lattice topological charge density, and the cooling method. They give 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 determine the string tension, without finding evidence of screening effects.