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

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

1995-07-14

arxiv.org/abs/hep-th/9507080v1

Physics

High Energy Physics

High Energy Physics - Theory

7 pages, LaTeX

Scientific paper

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 $\xi$, and the dynamical mass generation takes place only when $R0)$, which leads us to define a function looking like a natural generalization of Euler-Mascheroni constant.

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