Large-N ℂℙN − 1 sigma model on a finite interval: general Dirichlet boundary conditions

A bstract This is the third of the series of articles on the large- N two-dimensional ℂℙ N − 1 sigma model, defined on a finite space interval L with Dirichlet boundary conditions. Here the cases of the general Dirichlet boundary conditions are studied, where the relative ℂℙ N − 1 orientations at the two boundaries are generic, and numerical solutions are presented. Distinctive features of the ℂℙ N − 1 sigma model, as compared e.g., to an O ( N ) model, which were not entirely evident in the basic properties studied in the first two articles in the large N limit, manifest themselves here. It is found that the total energy is minimized when the fields are aligned in the same direction at the two boundaries.