We investigate the θ-dependence of two-dimensional CPN-1 models in the large-N limit by lattice simulations. Thanks to a recent algorithm proposed by M. Hasenbusch to improve the critical slowing down of topological modes, combined with simulations at imaginary values of θ, we manage to determine the vacuum energy density up the sixth order in θ and up to N=51. Our results support analytic predictions, which are known up to the next-to-leading term in 1/N for the quadratic term in θ (topological susceptibility), and up to the leading term for the quartic coefficient b2. Moreover, we give a numerical estimate of further terms in the 1/N expansion for both quantities, pointing out that the 1/N convergence for the θ-dependence of this class of models is particularly slow.

Large-N expansion and θ-dependence of 2D CPN-1 models beyond the leading order

Bonanno C.;D'elia M.
2019-01-01

Abstract

We investigate the θ-dependence of two-dimensional CPN-1 models in the large-N limit by lattice simulations. Thanks to a recent algorithm proposed by M. Hasenbusch to improve the critical slowing down of topological modes, combined with simulations at imaginary values of θ, we manage to determine the vacuum energy density up the sixth order in θ and up to N=51. Our results support analytic predictions, which are known up to the next-to-leading term in 1/N for the quadratic term in θ (topological susceptibility), and up to the leading term for the quartic coefficient b2. Moreover, we give a numerical estimate of further terms in the 1/N expansion for both quantities, pointing out that the 1/N convergence for the θ-dependence of this class of models is particularly slow.
2019
Berni, M.; Bonanno, C.; D'Elia, M.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1028605
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