θ dependence in the small- N limit of 2d CPN-1 models

We present a systematic numerical study of θ dependence around θ=0 in the small-N limit of 2d CPN-1 models, aimed at clarifying the possible presence of a divergent topological susceptibility in the continuum limit. We follow a twofold strategy, based on one side on direct simulations for N=2 and N=3 on lattices with correlation lengths up to O(102) and, on the other side, on the small-N extrapolation of results obtained for N up to 9. Based on that, we provide conclusive evidence for a finite topological susceptibility at N=3, with a continuum estimate ζ2χ=0.110(5). On the other hand, results obtained for N=2 are still inconclusive: They are consistent with a logarithmically divergent continuum extrapolation but do not yet exclude a finite continuum value, ζ2χ∼0.4, with the divergence taking place for N slightly below 2 in this case. Finally, results obtained for the nonquadratic part of θ dependence, in particular, for the so-called b2 coefficient, are consistent with a θ dependence, matching that of the dilute instanton gas approximation at the point where ζ2χ diverges.