Critical curvature of large-$N$ nonlinear $O(N)$ sigma model on $S^2$

K. H. Kim; Dae-Yup Song

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arXiv · hep-th/9507080

Critical curvature of large-$N$ nonlinear $O(N)$ sigma model on $S^2$

K. H. Kim·Dae-Yup Song

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Abstract

We study the nonlinear $O(N)$ sigma model on $S^2$ with the gravitational coupling term, by evaluating the effective potential in the large-$N$ limit. It is shown that there is a critical curvature $R_c$ of $S^2$ for any positive gravitational coupling constant $ξ$, and the dynamical mass generation takes place only when $R 0)$, which leads us to define a function looking like a natural generalization of Euler-Mascheroni constant.

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K. H. Kim, Dae-Yup Song. 1995-07-14. Critical curvature of large-$N$ nonlinear $O(N)$ sigma model on $S^2$. https://arxiv.org/abs/hep-th/9507080

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