Gap Equations of O(N) Non-linear Sigma Model in Three Dimensions

Details Gap Equations of O(N) Non-linear Sigma Model in Three Dimensions Gap Equations of O(N) Non-linear Sigma Model in Three Dimensions

1994-12-21

arxiv.org/abs/hep-th/9412183v1

Physics

High Energy Physics

High Energy Physics - Theory

10pages,Latex

Scientific paper

We study the $O(N)$ non-linear $\sigma$ model on three-dimensional manifolds of constant curvature by means of the large $N$ expansion at the critical point. We examine saddle point equations imposing anti-periodic boundary condition in time direction. In the case $S^1 \times S^2$ we find that a solution is inevitably unstable. We briefly refer to the case $S^1 \times S^1 \times S^1$.

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