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

Abstract

Abstract We investigate, by numerical simulations on a lattice, the θ-dependence of 2d CP N − 1 models for a range of N going from 9 to 31, combining imaginary θ 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 θ of the vacuum energy of the theory, parameterized in terms of the topological susceptibility χ 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 θ 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.