Phase transition by curvature in three dimensional $O(N)$ sigma model

Details Phase transition by curvature in three dimensional $O(N)$ sigma model Phase transition by curvature in three dimensional $O(N)$ sigma model

1995-05-06

arxiv.org/abs/hep-th/9505036v2

Mod.Phys.Lett. A11 (1996) 1569-1578

Physics

High Energy Physics

High Energy Physics - Theory

13pages, REVTeX, Many typos are corrected

Scientific paper

10.1142/S0217732396001569

Using the effective potential, the large-$N$ nonlinear $O(N)$ sigma model with the curvature coupled term is studied on $S^2\times R^1$. We show that, for the conformally coupled case, the dynamical mass generation of the model in the strong-coupled regime on $R^3$ takes place for any finite scalar curvature (or radius of the $S^2$). If the coupling constant is larger than that of the conformally coupled case, there exist a critical curvature (radius) above (below) which the dynamical mass generation does not take place even in the strong-coupled regime. Below the critical curvature, the mass generation occurs as in the model on $R^3$.

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