Large-$N$ ${\mathbb{CP}}^{N-1}$ sigma model on a finite interval: general Dirichlet boundary conditions

Abstract

This is the third of the series of articles on the large-$N$ two-dimensional ${\mathbb{CP}}^{N-1}$ 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 ${\mathbb{CP}}^{N-1}$ orientations at the two boundaries are generic, and numerical solutions are presented. Distinctive features of the ${\mathbb{CP}}^{N-1}$ 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.

Latex, 19 figures

References in corpus (4)

• Sign Flip in the Casimir Force for Interacting Fermion Systems
• Large-N CP(N-1) sigma model on a finite interval and the renormalized string energy
• Self-Consistent Large-$N$ Analytical Solutions of Inhomogneous Condensates in Quantum $\mathbb{C}{P}^{N-1}$ Model
• Monopole-vortex complex at large distances and nonAbelian duality

Cited by in corpus (9)

• Confinement-Deconfinement Crossover in the Lattice $\mathbb{C}{P}^{N-1}$ Model
• Lattice $\mathbb{C}{P}^{N-1}$ model with ${\mathbb{Z}}_N$ twisted boundary condition: bions, adiabatic continuity and pseudo-entropy
• Ground state modulations in the $\mathbb{C}{P}^{N-1}$ model
• Spin Statistics and Surgeries of Topological Solitons in QCD Matter in Magnetic Field
• Confining solitons in the Higgs phase of $\mathbb{C}{P}^{N-1}$ model: Self-consistent exact solutions in large-$N$ limit
• Large-$N$ ${\mathbb{CP}}^{N-1}$ sigma model on a Euclidean torus: uniqueness and stability of the vacuum
• The Casimir effect for nonlinear sigma models and the Mermin-Wagner-Hohenberg-Coleman theorem
• Remarks on the large-$N$ $\mathbb{C}{P}^{N-1}$ model
• Grassmannian and Flag sigma models on interval: phase structure and L-dependence