Large-N CP(N-1) sigma model on a finite interval: physical boundary effects

TL;DR

This paper investigates the two-dimensional CP(N-1) sigma model on a finite interval, analyzing boundary effects and phase behavior in the large N limit, revealing a smooth transition to the standard model and boundary condition compatibility.

Contribution

It provides a detailed analysis of boundary effects in the CP(N-1) sigma model on finite intervals, including numerical solutions and boundary condition compatibility in the large N limit.

Findings

Unique phase with Dirichlet boundary conditions smoothly approaches the standard model as L increases.

Numerical solutions satisfy both Dirichlet and Neumann boundary conditions.

The model exhibits a constant mass generation in the confinement phase.

Abstract

We analyze the two-dimensional CP(N-1) sigma model defined on a finite space interval L, with various boundary conditions, in the large N limit. With the Dirichlet boundary condition at the both ends, we show that the system has a unique phase, which smoothly approaches in the large L limit the standard 2D CP(N-1) sigma model in confinement phase, with a constant mass generated for the n(i) fields. We study the full functional saddle-point equations for finite L, and solve them numerically. The latter reduces to the well-known gap equation in the large L limit. It is found that the solution satisfies actually both the Dirichlet and Neumann conditions.