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arXiv · 1911.03384

Large-$N$ expansion and $\theta$-dependence of $2d$ $CP^{N-1}$ models beyond the leading order

Mario Berni·Claudio Bonanno·Massimo D'Elia
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Abstract

We investigate the $\theta$-dependence of 2-dimensional $CP^{N-1}$ 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 $\theta$, we manage to determine the vacuum energy density up the sixth order in $\theta$ 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 $\theta$ (topological susceptibility), and up to the leading term for the quartic coefficient $b_2$. 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 $\theta$-dependence of this class of models is particularly slow.

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Mario Berni, Claudio Bonanno, Massimo D'Elia. 2019-11-08. Large-$N$ expansion and $\theta$-dependence of $2d$ $CP^{N-1}$ models beyond the leading order. https://doi.org/10.1103/physrevd.100.114509

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