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 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.

We simulate 4d SU(N) pure-gauge theories at large N using a parallel tempering scheme that combines simulations with open and periodic boundary conditions, implementing the algorithm originally proposed by Martin Hasenbusch for 2d CPN–1 models. That allows to dramatically suppress the topological freezing suffered from standard local algorithms, reducing the autocorrelation time of Q2 up to two orders of magnitude. Using this algorithm in combination with simulations at non-zero imaginary θ we are able to refine state-of-the-art results for the large-N behavior of the quartic coefficient of the θ-dependence of the vacuum energy b2, reaching an accuracy comparable with that of the large-N limit of the topological susceptibility.

The spectral projectors method is a way to obtain a theoretically well posed definition of the topological susceptibility on the lattice. Up to now this method has been defined and applied only to Wilson fermions. The goal of this work is to extend the method to staggered fermions, giving a definition for the staggered topological susceptibility and testing it in the pure SU (3) gauge theory. Besides, we also generalize the method to higher-order cumulants of the topological charge distribution.