Abstract
We investigate, by numerical simulations on a lattice, the θ-dependence of 2d CPN − 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 b2 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 b4 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 b4 are compared to large-N predictions, as well as to results obtained for SU(Nc) Yang-Mills theories, for which a first numerical determination is provided in this study for the case Nc = 2.
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Bonanno, C., Bonati, C. & D’Elia, M. Topological properties of CPN − 1 models in the large-N limit. J. High Energ. Phys. 2019, 3 (2019). https://doi.org/10.1007/JHEP01(2019)003
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DOI: https://doi.org/10.1007/JHEP01(2019)003