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

TL;DR

This paper investigates how curvature influences phase transitions and mass generation in the three-dimensional $O(N)$ sigma model, revealing a critical curvature threshold affecting dynamical mass generation.

Contribution

It introduces an analysis of the $O(N)$ sigma model on curved space, showing how curvature affects phase transitions and mass generation, especially in the large-$N$ limit.

Findings

Mass generation occurs for any finite curvature in the conformally coupled case.

A critical curvature exists beyond which mass generation is suppressed.

Curvature influences phase transition behavior in the model.

Abstract

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 $R^3$.