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- W2883267205 abstract "We investigate, by numerical simulations on a lattice, the $theta$-dependence of 2$d$ $CP^{N-1}$ models for a range of $N$ going from 9 to 31, combining imaginary $theta$ 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 $theta$ of the vacuum energy of the theory, parameterized in terms of the topological susceptibility $chi$ 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 $theta$ 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 $N leq 11$, 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 $N_c = 2$." @default.
- W2883267205 created "2018-08-03" @default.
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- W2883267205 date "2019-01-01" @default.
- W2883267205 modified "2023-10-15" @default.
- W2883267205 title "Topological properties of CPN − 1 models in the large-N limit" @default.
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- W2883267205 doi "https://doi.org/10.1007/jhep01(2019)003" @default.
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