Topological properties of CPN-1 models in the large-N limit

We investigate, by numerical simulations on a lattice, the -dependence of 2d CPN - 1 models for a range of N going from 9 to 31, combining imaginary and simulated tempering techniques to improve the signal-to-noise ratio and alleviate the critical slowing down of the topological modes. We provide continuum extrapolations for the second and fourth order coefficients in the Taylor expansion in of the vacuum energy of the theory, parameterized in terms of the topological susceptibility and of the so-called b(2) coefficient. Those are then compared with available analytic predictions obtained within the 1/N expansion, pointing out that higher order corrections might be relevant in the explored range of N, and that this fact might be related to the non-analytic behavior expected for N = 2. We also consider sixth-order corrections in the expansion, parameterized in terms of the so-called b(4) coefficient: in this case our present statistical accuracy permits to have reliable non-zero continuum estimations only for N 11, while for larger values we can only set upper bounds. The sign and values obtained for b(4) are compared to large-N predictions, as well as to results obtained for SU(N-c) Yang-Mills theories, for which a first numerical determination is provided in this study for the case N-c = 2.