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arXiv · hep-th/9404055

Large-$N$ nonlinear $σ$ models on $R^2\times S^1$

Dae Yup Song
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Abstract

The large-$N$ nonlinear $O(N)$, $CP^{N-1}$ $σ$ models are studied on $R^2 \times S^1$. The $N$-components scalar fields of the models are supposed to acquire a phase $e^{i2πδ}$ $(0\leq δ<1)$, along the circulation of the circle, $S^1$. We evaluate the effective potentials to the leading order of the $1/N$ expansion. It is shown that, on $R^2\times S^1$ the $O(N)$ model has rich phase structure while the phase of $CP^{N-1}$ model is just that of the model at finite temperature.

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Dae Yup Song. 1994-04-10. Large-$N$ nonlinear $σ$ models on $R^2\times S^1$. https://doi.org/10.1103/physrevd.49.6794

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