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

Abstract

We investigate the $\theta$-dependence of 2-dimensional $C{P}^{N-1}$ 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.

References in corpus (8)

• Theta dependence of the vacuum energy in the SU(3) gauge theory from the lattice
• $\theta$ dependence of 4D $SU(N)$ gauge theories in the large-$N$ limit
• Fighting topological freezing in the two-dimensional CP${}^{N-1}$ model
• Susceptibility of the QCD vacuum to CP-odd electromagnetic background fields
• Mass gap in the 2D O(3) non-linear sigma model with a theta=pi term
• Behavior near $\theta =\pi$ of the mass gap in the 2D O(3) non-linear sigma model
• On the effective Lagrangian of CP^(N-1) models in the large N limit
• Theta-vacuum and large N limit in CP^{N-1} sigma models

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• Lattice determination of the topological susceptibility slope ${\chi }^{\prime }$ of $2d{\mathrm{CP}}^{N-1}$ models at large $N$
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• Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
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• Large $\theta$ angle in two-dimensional large $N$ ${\mathbb{CP}}^{N-1}$ model
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