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.
Publisher
Springer Science and Business Media LLC
Subject
Nuclear and High Energy Physics
Reference71 articles.
1. E. Witten, Instantons, the Quark Model and the 1/n Expansion, Nucl. Phys.
B 149 (1979) 285 [INSPIRE].
2. A. D’Adda, M. Lüscher and P. Di Vecchia, A 1/n Expandable Series of Nonlinear σ-models with Instantons, Nucl. Phys.
B 146 (1978) 63 [INSPIRE].
3. F. David, Instantons and Condensates in Two-dimensional CP
(N − 1)
Models, Phys. Lett.
B 138 (1984) 139 [INSPIRE].
4. M. Shifman, Advanced topics in Quantum Field Theory, Cambridge University Press, Cambridge U.K. (2012), pg. 171, pg. 361.
5. M. Campostrini and P. Rossi, 1/N expansion of the topological susceptibility in the CP
N − 1
models, Phys. Lett.
B 272 (1991) 305 [INSPIRE].
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