Large-N expansion and θ-dependence of 2D CPN-1 models beyond the leading order

We investigate the theta-dependence of two-dimensional CPN-1 models in the large-N limit by lattice simulations. Thanks to a recent algorithm proposed by M. Hasenbusch to improve the critical slowing down of topological modes, combined with simulations at imaginary values of theta, we manage to determine the vacuum energy density up the sixth order in theta and up to N = 51. Our results support analytic predictions, which are known up to the next-to-leading term in 1/N for the quadratic term in theta (topological susceptibility), and up to the leading term for the quartic coefficient b(2). Moreover, we give a numerical estimate of further terms in the 1/N expansion for both quantities, pointing out that the 1/N convergence for the theta-dependence of this class of models is particularly slow.