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.

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• Large-$N$ $SU(N)$ Yang-Mills theories with milder topological freezing
• $\theta$-dependence and center symmetry in Yang-Mills theories
• Lattice $\mathbb{C}{P}^{N-1}$ model with ${\mathbb{Z}}_N$ twisted boundary condition: bions, adiabatic continuity and pseudo-entropy
• Lattice determination of the topological susceptibility slope ${\chi }^{\prime }$ of $2d{\mathrm{CP}}^{N-1}$ models at large $N$
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