Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large-$N$ expansion and $\theta$-dependence of $2d$ $CP^{N-1}$ models
  beyond the leading order   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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The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
9
The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org